{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Sampling Of Monte Carlo Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook is an introduction to Monte Carlo methods.  Monte Carlo methods are a class of techniques that use random sampling to simulate a draw from some distribution.  By making repeated draws and calculating an aggregate on the distribution of those draws, it's possible to approximate a solution to a problem that may be very hard to calculate directly.\n",
    "\n",
    "Below we'll explore several examples of using Monte Carlo methods to model a domain and attempt to answer a question.  These examples are intentionally basic.  They're designed to illustrate the core concept without getting lost in problem-specific details.  Consider these a starting point for learning how to apply Monte Carlo more broadly.\n",
    "\n",
    "One key point that's worth stating - Monte Carlo methods are an <b>approach</b>, not an algorithm.  This was confusing to me at first.  I kept looking for a \"Monte Carlo\" python library that implemented everything for me like scikit-learn does.  There isn't one.  It's a way of thinking about a problem, similar to dynamic programming.  Each problem is different.  There may be some patterns but they have to be learned over time.  It isn't something that can be abstracted into a library.\n",
    "\n",
    "The application of Monte Carlo methods tends to follow a pattern.  There are four general steps, and you'll see below that the problems we tackle pretty much adhere to this formula.\n",
    "\n",
    "1) Create a model of the domain<br>\n",
    "2) Generate random draws from the distribution over the domain<br>\n",
    "3) Perform some deterministic calculation on the output<br>\n",
    "4) Aggregate the results<br>\n",
    "\n",
    "This sequence informs us about the type of problems where the general application of Monte Carlo methods is useful.  Specifically, when we have some <b>generative model</b> of a domain (i.e. something that we can use to generate data points from at will) and want to ask a question about that domain that isn't easily answered directly, we can use Monte Carlo to get the answer instead.\n",
    "\n",
    "To start off, let's tackle one of the simplest domains there is - rolling a pair of dice.  This is very straightforward to implement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n",
      "8\n",
      "9\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/john/anaconda/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import random\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "\n",
    "def roll_die():\n",
    "    return random.randint(1, 6)\n",
    "\n",
    "\n",
    "def roll_dice():\n",
    "    return roll_die() + roll_die()\n",
    "\n",
    "\n",
    "print(roll_dice())\n",
    "print(roll_dice())\n",
    "print(roll_dice())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Think of the dice as a probability distribution.  On any given roll, there's some likelihood of getting each possible number.  Collectively, these probabilites represent the distribution for the dice-rolling domain.  Now imagine you want to know what this distribution looks like, having only the knowledge that you have two dice and each one can roll a 1-6 with equal probability.  How would you calculate this distribution analytically?  It's not obvious, even for the simplest of domains.  Fortunately there's an easy way to figure it out - just roll the dice over and over, and count how many times you get each combination!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtYAAAIMCAYAAADRteuPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAHbZJREFUeJzt3X+s5Xdd5/HXezsWAcUWOrA4U3bqOqKF6FLHUiVrXCrtlBKmf0DSRmWCTSYxVdF1I+36RxOwm7Iaq0SpaehIcUlLU3E7scU6KbhkEygdflhaKs6kdNtrKx0ypbISwcH3/nG/416ndzoz937uPXNnHo/k5p7v5/v5nvs5OWF45tvv+Z7q7gAAAMvzb2a9AAAAOBkIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhg3awXsFRnnXVWb9q0adbLAADgJPaZz3zmq929/ljmrtmw3rRpU/bs2TPrZQAAcBKrqv9zrHNdCgIAAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMMC6WS8A4FS26eq7Zr2EFfPo9ZfOegkAq8oZawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABjhrWVbWzqp6qqgcPG/+lqvpSVT1UVf99wfg1VbVv2nfxgvGt09i+qrp6wfg5VXVfVe2tqg9X1emjXhwAAKyWYzlj/YEkWxcOVNV/SrItyQ9396uS/PY0fm6Sy5O8ajrmfVV1WlWdluQPklyS5NwkV0xzk+Q9SW7o7s1Jnk5y5XJfFAAArLajhnV3fyLJgcOGfyHJ9d39zWnOU9P4tiS3dfc3u/vLSfYlOX/62dfdj3T3t5LclmRbVVWS1ye5Yzr+liSXLfM1AQDAqlvqNdY/kOQ/Tpdw/K+q+rFpfEOSxxfMm5vGjjT+kiRf6+6Dh40DAMCasm4Zx52Z5IIkP5bk9qr6viS1yNzO4gHfzzF/UVW1I8mOJHnFK15xnEsGAICVs9Qz1nNJPtLzPp3kn5OcNY2fvWDexiRPPMf4V5OcUVXrDhtfVHff1N1bunvL+vXrl7h0AAAYb6lh/T8zf210quoHkpye+UjeleTyqnpeVZ2TZHOSTye5P8nm6Q4gp2f+A467uruTfDzJW6bn3Z7kzqW+GAAAmJWjXgpSVbcm+akkZ1XVXJJrk+xMsnO6Bd+3kmyfIvmhqro9yReTHExyVXd/e3qeX0xyT5LTkuzs7oemP/HOJLdV1W8m+VySmwe+PgAAWBVHDevuvuIIu372CPOvS3LdIuN3J7l7kfFHMn/XEAAAWLN88yIAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwwFHDuqp2VtVTVfXgIvv+S1V1VZ01bVdVvbeq9lXVA1V13oK526tq7/SzfcH4j1bVF6Zj3ltVNerFAQDAajmWM9YfSLL18MGqOjvJG5I8tmD4kiSbp58dSW6c5r44ybVJXpvk/CTXVtWZ0zE3TnMPHfesvwUAACe6o4Z1d38iyYFFdt2Q5NeT9IKxbUk+2PM+leSMqnp5kouT7O7uA939dJLdSbZO+17U3Z/s7k7ywSSXLe8lAQDA6lvSNdZV9eYkf9vdf3XYrg1JHl+wPTeNPdf43CLjAACwpqw73gOq6gVJfiPJRYvtXmSslzB+pL+9I/OXjeQVr3jFUdcKAACrZSlnrP99knOS/FVVPZpkY5LPVtW/zfwZ57MXzN2Y5ImjjG9cZHxR3X1Td2/p7i3r169fwtIBAGBlHHdYd/cXuvul3b2puzdlPo7P6+6/S7Irydumu4NckOSZ7n4yyT1JLqqqM6cPLV6U5J5p39er6oLpbiBvS3LnoNcGAACr5qiXglTVrUl+KslZVTWX5NruvvkI0+9O8sYk+5J8I8nbk6S7D1TVu5PcP817V3cf+kDkL2T+ziPPT/LR6QeANW7T1XfNegkr6tHrL531EoATzFHDuruvOMr+TQsed5KrjjBvZ5Kdi4zvSfLqo60DAABOZL55EQAABhDWAAAwwHHfbg9gNZ3s1+kCcPJwxhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAxw1LCuqp1V9VRVPbhg7Leq6q+r6oGq+tOqOmPBvmuqal9VfamqLl4wvnUa21dVVy8YP6eq7quqvVX14ao6feQLBACA1XAsZ6w/kGTrYWO7k7y6u384yd8kuSZJqurcJJcnedV0zPuq6rSqOi3JHyS5JMm5Sa6Y5ibJe5Lc0N2bkzyd5MplvSIAAJiBo4Z1d38iyYHDxv6iuw9Om59KsnF6vC3Jbd39ze7+cpJ9Sc6ffvZ19yPd/a0ktyXZVlWV5PVJ7piOvyXJZct8TQAAsOpGXGP980k+Oj3ekOTxBfvmprEjjb8kydcWRPqhcQAAWFOWFdZV9RtJDib50KGhRab1EsaP9Pd2VNWeqtqzf//+410uAACsmCWHdVVtT/KmJD/T3YdieC7J2QumbUzyxHOMfzXJGVW17rDxRXX3Td29pbu3rF+/fqlLBwCA4ZYU1lW1Nck7k7y5u7+xYNeuJJdX1fOq6pwkm5N8Osn9STZPdwA5PfMfcNw1BfnHk7xlOn57kjuX9lIAAGB2juV2e7cm+WSSV1bVXFVdmeT3k3x3kt1V9fmq+sMk6e6Hktye5ItJ/jzJVd397eka6l9Mck+Sh5PcPs1N5gP9P1fVvsxfc33z0FcIAACrYN3RJnT3FYsMHzF+u/u6JNctMn53krsXGX8k83cNAQCANcs3LwIAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGWDfrBQDLt+nqu2a9BAA45TljDQAAAwhrAAAYwKUgALAEJ/MlWI9ef+mslwBrkjPWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwwFHDuqp2VtVTVfXggrEXV9Xuqto7/T5zGq+qem9V7auqB6rqvAXHbJ/m762q7QvGf7SqvjAd896qqtEvEgAAVtqxnLH+QJKth41dneTe7t6c5N5pO0kuSbJ5+tmR5MZkPsSTXJvktUnOT3LtoRif5uxYcNzhfwsAAE54Rw3r7v5EkgOHDW9Lcsv0+JYkly0Y/2DP+1SSM6rq5UkuTrK7uw9099NJdifZOu17UXd/srs7yQcXPBcAAKwZS73G+mXd/WSSTL9fOo1vSPL4gnlz09hzjc8tMg4AAGvK6A8vLnZ9dC9hfPEnr9pRVXuqas/+/fuXuEQAABhvqWH9lekyjky/n5rG55KcvWDexiRPHGV84yLji+rum7p7S3dvWb9+/RKXDgAA4y01rHclOXRnj+1J7lww/rbp7iAXJHlmulTkniQXVdWZ04cWL0pyz7Tv61V1wXQ3kLcteC4AAFgz1h1tQlXdmuSnkpxVVXOZv7vH9Ulur6orkzyW5K3T9LuTvDHJviTfSPL2JOnuA1X17iT3T/Pe1d2HPhD5C5m/88jzk3x0+gEAgDXlqGHd3VccYdeFi8ztJFcd4Xl2Jtm5yPieJK8+2joAAOBE5psXAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAdbNegEAwIll09V3zXoJK+bR6y+d9RI4iTljDQAAAwhrAAAYQFgDAMAAwhoAAAbw4UVOGSfzh3EAgNlzxhoAAAYQ1gAAMMCywrqqfrWqHqqqB6vq1qr6zqo6p6ruq6q9VfXhqjp9mvu8aXvftH/Tgue5Zhr/UlVdvLyXBAAAq2/JYV1VG5L8cpIt3f3qJKcluTzJe5Lc0N2bkzyd5MrpkCuTPN3d35/khmlequrc6bhXJdma5H1VddpS1wUAALOw3EtB1iV5flWtS/KCJE8meX2SO6b9tyS5bHq8bdrOtP/Cqqpp/Lbu/mZ3fznJviTnL3NdAACwqpYc1t39t0l+O8ljmQ/qZ5J8JsnXuvvgNG0uyYbp8YYkj0/HHpzmv2Th+CLHAADAmrCcS0HOzPzZ5nOSfG+SFya5ZJGpfeiQI+w70vhif3NHVe2pqj379+8//kUDAMAKWc6lID+d5Mvdvb+7/ynJR5L8RJIzpktDkmRjkiemx3NJzk6Saf/3JDmwcHyRY/6V7r6pu7d095b169cvY+kAADDWcsL6sSQXVNULpmulL0zyxSQfT/KWac72JHdOj3dN25n2f6y7exq/fLpryDlJNif59DLWBQAAq27J37zY3fdV1R1JPpvkYJLPJbkpyV1Jbquq35zGbp4OuTnJH1fVvsyfqb58ep6Hqur2zEf5wSRXdfe3l7ouAACYhWV9pXl3X5vk2sOGH8kid/Xo7n9M8tYjPM91Sa5bzloAAGCWfPMiAAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMMCywrqqzqiqO6rqr6vq4ar68ap6cVXtrqq90+8zp7lVVe+tqn1V9UBVnbfgebZP8/dW1fblvigAAFhtyz1j/XtJ/ry7fzDJjyR5OMnVSe7t7s1J7p22k+SSJJunnx1JbkySqnpxkmuTvDbJ+UmuPRTjAACwViw5rKvqRUl+MsnNSdLd3+ruryXZluSWadotSS6bHm9L8sGe96kkZ1TVy5NcnGR3dx/o7qeT7E6ydanrAgCAWVjOGevvS7I/yR9V1eeq6v1V9cIkL+vuJ5Nk+v3Saf6GJI8vOH5uGjvSOAAArBnLCet1Sc5LcmN3vybJP+T/X/axmFpkrJ9j/NlPULWjqvZU1Z79+/cf73oBAGDFLCes55LMdfd90/YdmQ/tr0yXeGT6/dSC+WcvOH5jkieeY/xZuvum7t7S3VvWr1+/jKUDAMBYSw7r7v67JI9X1SunoQuTfDHJriSH7uyxPcmd0+NdSd423R3kgiTPTJeK3JPkoqo6c/rQ4kXTGAAArBnrlnn8LyX5UFWdnuSRJG/PfKzfXlVXJnksyVunuXcneWOSfUm+Mc1Ndx+oqncnuX+a967uPrDMdQEAwKpaVlh39+eTbFlk14WLzO0kVx3heXYm2bmctQAAwCz55kUAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAyw3PtYAwCsGZuuvmvWS1hRj15/6ayXcEoT1vyLk/0fGwCAleRSEAAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYIBlh3VVnVZVn6uqP5u2z6mq+6pqb1V9uKpOn8afN23vm/ZvWvAc10zjX6qqi5e7JgAAWG0jzli/I8nDC7bfk+SG7t6c5OkkV07jVyZ5uru/P8kN07xU1blJLk/yqiRbk7yvqk4bsC4AAFg1ywrrqtqY5NIk75+2K8nrk9wxTbklyWXT423Tdqb9F07ztyW5rbu/2d1fTrIvyfnLWRcAAKy25Z6x/t0kv57kn6ftlyT5WncfnLbnkmyYHm9I8niSTPufmeb/y/gixwAAwJqw5LCuqjcleaq7P7NweJGpfZR9z3XM4X9zR1Xtqao9+/fvP671AgDASlrOGevXJXlzVT2a5LbMXwLyu0nOqKp105yNSZ6YHs8lOTtJpv3fk+TAwvFFjvlXuvum7t7S3VvWr1+/jKUDAMBYSw7r7r6muzd296bMf/jwY939M0k+nuQt07TtSe6cHu+atjPt/1h39zR++XTXkHOSbE7y6aWuCwAAZmHd0acct3cmua2qfjPJ55LcPI3fnOSPq2pf5s9UX54k3f1QVd2e5ItJDia5qru/vQLrAgCAFTMkrLv7L5P85fT4kSxyV4/u/sckbz3C8dcluW7EWgAAYBZ88yIAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYIB1s14AAABjbLr6rlkvYcU8ev2ls17CUTljDQAAAwhrAAAYQFgDAMAArrE+TifztUsAACydM9YAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAZYclhX1dlV9fGqeriqHqqqd0zjL66q3VW1d/p95jReVfXeqtpXVQ9U1XkLnmv7NH9vVW1f/ssCAIDVtZwz1geT/Fp3/1CSC5JcVVXnJrk6yb3dvTnJvdN2klySZPP0syPJjcl8iCe5Nslrk5yf5NpDMQ4AAGvFksO6u5/s7s9Oj7+e5OEkG5JsS3LLNO2WJJdNj7cl+WDP+1SSM6rq5UkuTrK7uw9099NJdifZutR1AQDALAy5xrqqNiV5TZL7krysu59M5uM7yUunaRuSPL7gsLlp7EjjAACwZiw7rKvqu5L8SZJf6e6/f66pi4z1c4wv9rd2VNWeqtqzf//+418sAACskGWFdVV9R+aj+kPd/ZFp+CvTJR6Zfj81jc8lOXvB4RuTPPEc48/S3Td195bu3rJ+/frlLB0AAIZazl1BKsnNSR7u7t9ZsGtXkkN39tie5M4F42+b7g5yQZJnpktF7klyUVWdOX1o8aJpDAAA1ox1yzj2dUl+LskXqurz09h/TXJ9ktur6sokjyV567Tv7iRvTLIvyTeSvD1JuvtAVb07yf3TvHd194FlrAsAAFbdksO6u/93Fr8+OkkuXGR+J7nqCM+1M8nOpa4FAABmzTcvAgDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAMIawAAGEBYAwDAAMIaAAAGENYAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABhDWAAAwgLAGAIABhDUAAAwgrAEAYABhDQAAAwhrAAAYQFgDAMAAwhoAAAYQ1gAAMICwBgCAAYQ1AAAMIKwBAGAAYQ0AAAOcMGFdVVur6ktVta+qrp71egAA4HicEGFdVacl+YMklyQ5N8kVVXXubFcFAADH7oQI6yTnJ9nX3Y9097eS3JZk24zXBAAAx+xECesNSR5fsD03jQEAwJqwbtYLmNQiY/2sSVU7kuyYNv9vVX1pRVe1uLOSfHUGf5fV5X0+NXifT37e41OD9/kUUO+Z2fv874514okS1nNJzl6wvTHJE4dP6u6bkty0WotaTFXt6e4ts1wDK8/7fGrwPp/8vMenBu/zqWEtvM8nyqUg9yfZXFXnVNXpSS5PsmvGawIAgGN2Qpyx7u6DVfWLSe5JclqSnd390IyXBQAAx+yECOsk6e67k9w963Ucg5leisKq8T6fGrzPJz/v8anB+3xqOOHf5+p+1mcEAQCA43SiXGMNAABrmrA+RlV1dlV9vKoerqqHquods14TK6OqTquqz1XVn816LayMqjqjqu6oqr+e/jf947NeE+NV1a9O/14/WFW3VtV3znpNLF9V7ayqp6rqwQVjL66q3VW1d/p95izXyPId4X3+renf7Qeq6k+r6oxZrnExwvrYHUzya939Q0kuSHKVr10/ab0jycOzXgQr6veS/Hl3/2CSH4n3+6RTVRuS/HKSLd396sx/MP7y2a6KQT6QZOthY1cnube7Nye5d9pmbftAnv0+707y6u7+4SR/k+Sa1V7U0QjrY9TdT3b3Z6fHX8/8/xH7dsiTTFVtTHJpkvfPei2sjKp6UZKfTHJzknT3t7r7a7NdFStkXZLnV9W6JC/IIt+PwNrT3Z9IcuCw4W1Jbpke35LkslVdFMMt9j53919098Fp81OZ/96TE4qwXoKq2pTkNUnum+1KWAG/m+TXk/zzrBfCivm+JPuT/NF0yc/7q+qFs14UY3X33yb57SSPJXkyyTPd/RezXRUr6GXd/WQyfyIsyUtnvB5W3s8n+eisF3E4YX2cquq7kvxJkl/p7r+f9XoYp6relOSp7v7MrNfCilqX5LwkN3b3a5L8Q/xn45POdI3ttiTnJPneJC+sqp+d7aqAEarqNzJ/ie6HZr2Wwwnr41BV35H5qP5Qd39k1uthuNcleXNVPZrktiSvr6r/MdslsQLmksx196H/4nRH5kObk8tPJ/lyd+/v7n9K8pEkPzHjNbFyvlJVL0+S6fdTM14PK6Sqtid5U5Kf6RPwntHC+hhVVWX+msyHu/t3Zr0exuvua7p7Y3dvyvyHnD7W3c5wnWS6+++SPF5Vr5yGLkzyxRkuiZXxWJILquoF07/fF8aHVE9mu5Jsnx5vT3LnDNfCCqmqrUnemeTN3f2NWa9nMcL62L0uyc9l/izm56efN856UcCS/FKSD1XVA0n+Q5L/NuP1MNj0XyTuSPLZJF/I/P/fnfDf2sbRVdWtST6Z5JVVNVdVVya5PskbqmpvkjdM26xhR3iffz/JdyfZPXXYH850kYvwzYsAADCAM9YAADCAsAYAgAGENQAADCCsAQBgAGENAAADCGsAABhAWAMAwADCGgAABvh/XYQwpsa8CYYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb8dce45438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def roll_histogram(samples):\n",
    "    rolls = []\n",
    "    for _ in range(samples):\n",
    "        rolls.append(roll_dice())\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(12, 9))\n",
    "    plt.hist(rolls, bins=11)\n",
    "\n",
    "\n",
    "roll_histogram(100000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The histogram gives us a visual sense of the likelihood of each roll, but what if we want something more targeted?  Say, for example, that we wanted to know the probability of rolling a 6 or higher?  Again, consider how you would solve this with an equation.  It's not easy, right?  But with a few very simple lines of code we can write a function that makes this question trivial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prob_of_roll_greater_than_equal_to(x, n_samples):\n",
    "    geq = 0\n",
    "    for _ in range(n_samples):\n",
    "        if roll_dice() >= x:\n",
    "            geq += 1\n",
    "\n",
    "    probability = float(geq) / n_samples\n",
    "    print('Probability of rolling greater than or equal to {0}: {1} ({2} samples)'.format(x, probability, n_samples))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All we're doing is running a loop some number of times and rolling the dice, then recording if the result is greater than or equal to some number of interest.  At the end we calculate the proportion of samples that matched our critera, and we have the probability we're interested in.  Easy!\n",
    "\n",
    "You might notice that there's a parameter for the number of samples to draw.  This is one of the tricky parts of Monte Carlo.  We're relying on the [law of large numbers](https://en.wikipedia.org/wiki/Law_of_large_numbers) to get an accurate result, but how large is large enough?  In practice it seems you just have to tinker with the number of samples and see where the result begins to stabilize (think of it as a hyperparameter that can be tuned).\n",
    "\n",
    "To make this more concrete, let's try calculating the probability of a 6 or higher with varying numbers of samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of rolling greater than or equal to 6: 0.9 (10 samples)\n",
      "Probability of rolling greater than or equal to 6: 0.68 (100 samples)\n",
      "Probability of rolling greater than or equal to 6: 0.723 (1000 samples)\n",
      "Probability of rolling greater than or equal to 6: 0.7217 (10000 samples)\n",
      "Probability of rolling greater than or equal to 6: 0.72135 (100000 samples)\n",
      "Probability of rolling greater than or equal to 6: 0.722335 (1000000 samples)\n"
     ]
    }
   ],
   "source": [
    "prob_of_roll_greater_than_equal_to(6, n_samples=10)\n",
    "prob_of_roll_greater_than_equal_to(6, n_samples=100)\n",
    "prob_of_roll_greater_than_equal_to(6, n_samples=1000)\n",
    "prob_of_roll_greater_than_equal_to(6, n_samples=10000)\n",
    "prob_of_roll_greater_than_equal_to(6, n_samples=100000)\n",
    "prob_of_roll_greater_than_equal_to(6, n_samples=1000000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case 100 samples wasn't quite enough, but 1,000,000 was probably overkill.  This is going to vary depending on the problem though.\n",
    "\n",
    "Let's move on to something slightly more complicated - calculating the value of pi.  If you're not aware, pi is the ratio of a circle's circumference to its diameter.  In other words, if you \"un-rolled\" a circle with a diameter of one you would get a line with a lenth of pi.  There are analytical ways to derive the value of pi, but what if we didn't know that?  What if all we knew was the definition above?  Monte Carlo to the rescue!\n",
    "\n",
    "To understand the function below, imagine a unit circle inscribed in a unit square.  We know that the area of a unit circle is pi/4, so if we generate a bunch of points randomly in a unit square and record how many of them \"hit\" in the circle's area, the ratio of \"hits\" to \"misses\" should be equal to pi/4.  We then multiply by 4 to get an approximation of pi.  This works with a full circle as well as a quarter circle (which we'll use below)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate_pi(samples):\n",
    "    hits = 0\n",
    "    for _ in range(samples):\n",
    "        x = random.random()\n",
    "        y = random.random()\n",
    "\n",
    "        if math.sqrt((x ** 2) + (y ** 2)) < 1:\n",
    "            hits += 1\n",
    "\n",
    "    ratio = (float(hits) / samples) * 4\n",
    "    print('Estimate with {0} samples: {1}'.format(samples, ratio))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try it out with varying numbers of samples and see what we get."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate with 10 samples: 3.2\n",
      "Estimate with 100 samples: 3.12\n",
      "Estimate with 1000 samples: 3.172\n",
      "Estimate with 10000 samples: 3.1352\n",
      "Estimate with 100000 samples: 3.14964\n",
      "Estimate with 1000000 samples: 3.14116\n"
     ]
    }
   ],
   "source": [
    "estimate_pi(samples=10)\n",
    "estimate_pi(samples=100)\n",
    "estimate_pi(samples=1000)\n",
    "estimate_pi(samples=10000)\n",
    "estimate_pi(samples=100000)\n",
    "estimate_pi(samples=1000000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We should observe that as we increase the number of samples, the result is converging on the value of pi.  If the logic I described above for how we're getting this result isn't clear, a picture might help."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_pi_estimate(samples):\n",
    "    hits = 0\n",
    "    x_inside = []\n",
    "    y_inside = []\n",
    "    x_outside = []\n",
    "    y_outside = []\n",
    "\n",
    "    for _ in range(samples):\n",
    "        x = random.random()\n",
    "        y = random.random()\n",
    "\n",
    "        if math.sqrt((x ** 2) + (y ** 2)) < 1:\n",
    "            hits += 1\n",
    "            x_inside.append(x)\n",
    "            y_inside.append(y)\n",
    "        else:\n",
    "            x_outside.append(x)\n",
    "            y_outside.append(y)\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(12, 9))\n",
    "    ax.set_aspect('equal')\n",
    "    ax.scatter(x_inside, y_inside, s=20, c='b')\n",
    "    ax.scatter(x_outside, y_outside, s=20, c='r')\n",
    "    fig.show()\n",
    "\n",
    "    ratio = (float(hits) / samples) * 4\n",
    "    print('Estimate with {0} samples: {1}'.format(samples, ratio))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function will plot randomly-generated numbers with a color coding indicating if the point falls inside (blue) or outside (red) the area of the unit circle.  Let's try it with a moderate number of samples first and see what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate with 10000 samples: 3.1244\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/john/anaconda/lib/python3.6/site-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
      "  \"matplotlib is currently using a non-GUI backend, \"\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhEAAAIMCAYAAABL1v5XAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAIABJREFUeJzsvW2IrVl2Hrar6nzWx50/nYBiaxgbgomDf2Q0xpLxoMGj6XFk5oKkXA0zWN3mXuHbgutLSBu6NCHd4KJ/FQ6hkpByOoSCmAr1Q786wa5AnD+VEMrjiWNbBQqyScDYcDqMxjZtWYymd368/fRZZ51nfez3nOrWpN4FL9331Dnvu9+91157rWd97dRay0ADDTTQQAMNNFAr7X7WAxhooIEGGmiggX48aVAiBhpooIEGGmigXjQoEQMNNNBAAw00UC8alIiBBhpooIEGGqgXDUrEQAMNNNBAAw3UiwYlYqCBBhpooIEG6kWDEjHQQAMNNNBAA/WiQYkYaKCBBhpooIF60aBEDDTQQAMNNNBAvWhQIgYaaKCBBhpooF40+qwe/Morr9QvfOELn9XjBxpooIEGGmggQn/37/7d/7fW+m9kvvuZKRFf+MIXyne/+93P6vEDDTTQQAMNNBChnZ2d/yf73cGdMdBAAw000EAD9aJBiRhooIEGGmiggXrRoEQMNNBAAw000EC9aFAiBhpooIEGGmigXjQoEQMNNNBAAw00UC8alIiBBhpooIEGGqgXDUrEQAMNNNBAAw3UiwYlYqCBBhpooIEG6kWDEjHQQAMNNNBAA/WiQYkYaKCBBhpooIF60aBEDDTQQAMNNNBAvWhQIgYaaKCBBhpooF40KBEDDTTQQAMNNFAvGpSIgQYaaKCBBhqoFw1KxEADDTTQQAMN1IsGJWKggQYaaKCBBupFgxIx0EADDTTQQAP1okGJGGiggQYaaKCBelGoROzs7Py3Ozs7i52dnX9o/H1nZ2fnbGdn57d3dnb+/s7Ozhe3P8yBBhpooIEGGugPGmWQiItSyp9z/v7vl1L+7Y+vv1RK+a82H9Zm9MEHpfydv9P998eC7nPAH3xQyv/0P3XXj82E/P+EfuwYMaDM+3wW79z6zB/HdflxHHMrRe+4rTnI3uchzPk2qNYaXqWUL5RS/qHxt79eSvmW+PdvlVJ+IrrnT/3UT9X7oMvLWufzWj/3ue6/l5f97rNY1Hp72/13K2TdMBrwJgO5vKx1PK61lO6aTFbvv/WXNEg/B/++u7vf539a78coy4iZMX6W7wHKvA/7zn2PHc88OMht+G0JCI8Wi1qvr7trG++9jTHf3dV6cdH9d1Pqs6bRb6J3bJkD71n6PufnfK3Oz2udTms9Oro/PsmO+TOgUsp3a0I3qN3JsrES8T+UUv6M+Pf/XEr5UnTP+1AiFotuvXFmltL9u3Vd+uxZlwesG0YD3kR4LBa1zmar9y6l+2yxuIeXNL57fr76nBcvujFMp8v3zQiFFqG8WNR6ctI9Z1uHReu7ZxhRrsFs1o1ZK1qYv6Ojbs7Oz/Pj2ZZgyrwP+85ksroG5+f2ePocvItF9wz9TEs53ZaAiA4pOabxuP+Bt40xLxa1Pnmy+vsnT/rzRB+5gd9oHpZj9N6xZQ6YkoD5tWSiNrLOz9f/1odPstQ6p5+CwvFpKxH/I1Eifsr47l8qpXy3lPLdz3/+81t/8dvbbh3k2j961H2eJcavs5kv21we8DaAN+BNhcftbWedsc3y+uvrmym6dwujS6FhbdjsJm0Vynj2NoVAq1VirevV1dIaZOuLcb544c/fs2f9UIG+lNlY7Dvs0nMIhc9DzCRJAXp9bR8G7L23ISC8ebXWFIp7y722MebLS/vQnM3WkaIIIewjHK05kYpE9I7ZObCeBZ77xjdi/pzN1hVT3KOFT7LUKuc/DSSt1k9difgD487YhqFhyUILLbX21SfPbFQUPhIKxu/NV3/3r2eP6m9e3PrvIwWBp3XryxNMLRNrbeToOjjohJG+l4em6O9eX9vv3HpYgPpYJWwO9vZW//3kSZuS5V3z+arg35bF7b1PBomIxnx+bq9XhNzM57UeH+eegzm5vt7cqvd+bynuBwfLtWldI7YH5vNab25WFVLtLmTvqq/xeKms7u3VOhotn8UQQks47u9zhAG/YXw+na6OV7+j3OPZucoqst41nfJ52929H8v/5CQvq7a9rx36tJWIP19K+ZullJ1Syk+XUm4z97zvmIhHj7r/SoRYkoUILRarRlEk2yy+xXO/d73oFAPxx9+fzusHd4tPBvzDybz+oDyqH5Z5/ZXxZb28rPWDu0X9sKz+7sMyr184WNgKqBCyH83n9Z89eVE/0odX9sXkhFxcrAuCo6Naz87WrZBNNrJ+MbbBpFDW720hL9Fm85gBbhd5HR6uPp/9XjJiizLXd96m0+XhenKyucWtKRN7oDeft5EAbVt/12tsaeveM/DeJydL5WM87ixNjDFCPO7ulm6W62vfILCU2Nls3a2XXSOGxH3ta6u/291d3vfp025e9/e3x1veYa4v5qpg6ywte/2OpXT/lq4IzVts3SJ3xabX6Wm7K8H7vjVeS1ZtA0lL0laViFLKf19K+WellB+WUv5JKeVZKeWNUsobH/99p5TyX5ZS/lEp5R9k4iFqvT8lotYlQmq5xCNEkqFZkvcvLnwlGnsdz/+Vcaco/N68UxRem1yuoIk/OVvUL5Xb+kpZfMJDV1e1vja5rB+WpYLxzXJp8xnZ4B+Wef3K5Kb+/sgR1tC8vUMhspili8ESNIeHbULLEwiwUrIW13RqHxYeM1hW1Gi0DFCLmOn2tlO27kuwWfOzbYsF0PjBwRIKZySFJuaGrT3cQxEfyLVgAhQbHePSSsV8zq3cjH9Sz+FotI4ojcerCsJ43H2P/b11jdhe8hSv+7j0IRUp7BJhADE0bzy2ERl5SfdXdIAzZWSb195ed/+sW9OLhbu95UppKR1PW3vrxxWJuI/rvpUIa64ziGRkSEseurxclyvs+sPTRf3pvaWigH3E+Gg+X+6FV8qqgiH39vW12FNk4D8oj+qXym39C3uX9UdT40BGIFpmEr1Lwo/aajg/52iGNbkXF7W+9Za9kTHxEfoAoabdJBlGieZgMuksEy3U2aa+u8vPI95R/vtnfmYJPVvvqJkD1ndkcev50EK6rxtA+9dxkEqe8OY24zeUm9qyWI+P13mEuc6853gXrAW9F66uustCMA4P4zViwqiPpd3HvWjtB4nOZFA68L9UrLDGuF8GudQuu5Z1ixQvtoatc8PGw9xQUuFkSu9s5sek9NnXPejBKxEe6hMhQhYvsrOKGTmt19VVvz2uA99/45wjEVA+/tBkUX/rq2+s34jAYYtFrb95cVt//7DBLcHgZ+2njaBnb7Lx0l5QYutGz8CDVqCmdVnw4osXmzHKwUH3/kzoWEGyLdArs5qAPjAmx3uy1MHIApPKJlCE6bQ78DMIQdYV4SkqDE2xXHfRumh+PTys9fnz7p2wbvoQLaUbn46T0HtmUyRiMumETKug0gglW9MoXgiHHkMHvABy6xqP7YBCTxmZTjuF33rO4WE/hIcpTCDmio2eM5ksg6p1dolWPiw//ZbowSsRlhJoIRHTKZeBkFVPn/Lzj8kP3I/JDHZdX6+fL/pZBwedfPXczfN5rf/8/LJ+NOfuj1I6t8lHQVYG3v3fGq/HZLiXDoSSVigsF0+JyPhwAfN5AgOQY0ZTzyAR19e1vvtuXshoi0keDDc3OdjKg2SBSMj3yx6urfPgMTE2hvzsxQs7doEpB601HiRvRQL07i5eM7nWfTKKcI++loTcM1YGkHQJIXjx8eP8MxCjYLlo2PXtb8fKDNYUaNzh4arbAW6mlrnHMzJ7LeP6wQXY9uyMjwnz2rqWzHXjjQWuEG/fs3e3LNhBibg/JUK7xoCAy79LnsX/M3f23Z3Nm4znoJBYMYH6urmJ97U2LL34rrpY1L/6jXX3B3jx7x3bB46OB/lmWcZk/F7Zqx9ZA5QxEXpyccNIMPz0T+cmAQP1LMxsEavLSzu1UP8te8n0SyAHkfWmx+8JMghEXVOhNeBLLjqzvj1Xw3zeHR7s71dXfgT/6am9sebz1ayDvu91eZk7iCJrOHOP8/MlotIHUjw5sS16rK9UMCaTWnd2/HtKZEfO2/l5jqf1ARWlrOkAyOggZjFK2vCIMm+sIFS2BgimtcaFecoonnrtGVnzBUuwlUey779FetBKhCUPnj5d/c7V1brBx5Q7ix+wDywjMIvSPX++Lr+n06XS2lqbJTqjPnF9EMHM0u4Rk/HHyl39sBCN6eoqd7j3vawgpmzmhpy0jHUFba2PdQnh7U0+OxTGY44ssIBE7VfdxC/ax/oej5cuDPb373wnPqimU55Kp3/36qvt79nH1cU2OWJzgKK9+y6/x/X18uDsA4nPZl12hcVPVt0C6zo+5lHlLfOiY0aiw9WDednaZ6pm3t35721Z4hIFefQo5sXRaDVjJjNHVjqrx4NAKDG2bKD5pvPYkx60EuHVWLq78+PxsvVL9PpZbs1MxpuFGI/HHYJinaHaBQIkuQ8SCLJq9+B6fXpZf3/qwObbyNPWAtELpGIvy16O+XOjwBnLTxVtbO9A1sE3QBMYcqL9+l5Aooaq2H30M/oqfAcH3eF6c7O9dc5eGQg3y4PSGo7cWt7muLrqh1jh2lYqZilLFI69i5UJwOJs8Bup0HquBi/gTI8vowjimVDkkfHiuSmZkXB93aaARd+dTPKxCFr461gHIFB9s22ACA6BldsnL37v7MyXm5aMyrqc2VkleTvr4vDGhr3BjOizszhZQe75lrnDGD64c+DlzMEE5s++sEeeO8IbE6wC63OvaBXT+vb37QPeeicvNZTNqyxWxMZ9fLwM5IOl5PntrPTVzAXN9tVX+zM0mHY6zVmMYNyVlCRjriL+Apqiecnb5NrXh+vlS/sZpSxRBrip9HtuK2UzUo6vrtafBWvIckEwdAWuAcbX1tx7gYAZhBD7TpdNhzA8Pub5/JvwuL6m005xlm7EyNXm+cQxZ3d3Nu9nAuvuKTbiQSsRXsql5a7F3sjKcevvkTETIXSR/ATaZikKllGj0VKP72TAvL7PixfJBZBWBF4YPuPooG1teCMtemaBX12tvwy0KFgCCAqT1sJoFPue8V5nZ+t1Ix494q4Kj1lkYSNrgVrSRS3h5MU0tFyIYTg7y0cSs3e+vc0hGwgqjRQvrRDoDTAa5Q40TcxXaCkB3/zm6pzs7a0qdhJZ2qS2wXi83nNF8xbiAZgyCbq+zqMiGC+7j3w/KA9WjJKFEFoHv1bCPf7GIe8paVmehWzQgXZetoikKAssiv8Yj5cGgv7bj0Oxqfu6Pq2y17iePvX/Hil0kXyJ+EQbhVDys3zsxQVlf5sN3rfQDj1H5pwIDfz717f17191/12zwvFC8I97DZpaKIpEl8oMAk+8FDDvkj5VlsrIJsnK/5far9U/4vZ2M/hcCia2SVoOtMj9g0sf4lAGANVBcdLZHpqJWUpSZAW2FvTxyErby66HjLnRqa6wDqQy683p/n6nvHnQKTI6WI0GxDJhLH2USssvr326Mo0XCo8Vk+TFX8jy4VHw8e1t92xPwD554j9LKkGRbPBiFLz4K/zdiovB+2CPREJ5S/RglQiG9GKepYvPcqVbCp2MP7NiajwkwlJeDg+7/ayREybHLV7PKBYHB7W+957fCVjLtaxS1NIDagXRtHz1m1IEZ8t0Lv35ptCntaGzkG3mfq2Fq7IXBPTdXS4NNcPge3vd5wzCB4yuSzq/fMmZmqFCGSvMOnAywlcrg9Z9vB4gbI6jZ+HfVsE1a/zyHkDZLHRB1h3py/fR/Fv+UQgDS7mzFBocvJHSarkr2ffef5//TQaMe+5NeXkxE5Hr1VPimBt0KDZ1P0pEJF+xFhZy2lK4kSkS1vpG8Ubz+bK43c1N3k2KwnhZhIKhj3LcUTC3d2YwlMJyj1qAQ4T2pCiabFhDrIKgN/EZqNdLO9Pa1rNn8f1Y46bb2/yCA4LKMpSsKeDFhDABJq3p8bjWd97x85GtcuUtkFvWCrOaHHnxFUwD9hCNzEa0unky8jZQtIlbMzr6XtH8e5Ha87ltzVmHNubaQyIQvJkJsH30qLOsGEoA3ojcr9a7ZWOzgNZY81HKMi1aKpjbNLwIPVglwkIiJM8AfWVuw6srjjwzRX1vL+9WjQzPqOutvmRtHmbMvXgR13mRdaAi3tZnxvW1HWYg5817D10SX/ZIkp8375WMlS9dKfIzy6IcjTrm0JkSEbxuCY4sdCzdLrLBUvQ7GbkNd0Fr2g6zgg8P1w9eWbGSWdNeFLClmH31q/FYvX4oGZ7w4iss+FkfzCg2lKmNwIKuPAZnG2g+5y6MLLLVekWIlJfmWKuvRBwc1PrlL69/bimYem/p9LS9vTg2hPE7C1RDN1MPodnb8+dHClmsc4syLfkOzfU+hUqVoAerRCwWcWoxYtc8d7l2b1v3tMrvM4pS/1t4H7VRPOWWHfRaHgLR1PeQaeLMfcvk5WTSoSjZtZCy1bofYomymWFrk235Q73eEh6UqjUbD1pcLLrDlZVEzvjQ0cWw9XCYTFY7xMk5iQ46LLxnBUs/OqtYqddAd87E/3sCejbzfdmW/5mV4NbjQcCfVyTG0oCtTpPWGj19agfKRj5Sbw3uM7Ua2j1iAbxNHAlAy53hXZEFY80NQ3msNEtphbWOEbEokQsLwZCyfDUT1lkFX//untwYoAetRHj88OxZt16IYcu2/LaCZ4+P28fHUv8ZMpmp7eLFLWxqnLTINXnhHOkjP7wLTf/S5AVoSb+M9HlHG5rBt8wSxwKze7EiS7gAh+HQub1tL0rjQcxRFHgpS2vHgu69Qiul2L1N4HvLMOWjR7W+/ro9R0yAssIpmjCnXsZOltHlemayCfQ4Mj5SzDW7ry4pz5AW75Bjhc6Yn9GrXhcpERomzVwy4NVCaqKALflbiQbIIM8Wtweb+z4uDib4PR+8lw4/FJu6P3eGxQ9sLXZ2/LgjGHSLBTeMmPKbheBxZlnZfN4Z6CkKUm6xjBBrT1sHvpRr2f2GfbvNulMZmZViBgaDRwcjm3goCxBKKIYTBal961u2cNeHSCZuAhdqVVgWSkt+sdWmOiM8Ly5sIX9xwWNRmFuIIUKsvgPezWJETRYiow/8DHKD8UcblfEm4xN0nJXjYJAiIG6sBVxruhjTYtGVxGVje/58XZG2yFoL7zdMOE0mPg9qgWqNLSv4MkFed3e5dZb+1z7CTcsOiXqx54/HcU+EFpdeIz1YJaKP9e1Zy7KRnVUoSirOLfWDWrIbLHknYwm07NAZhjjYr674e+AMZHMgDfXMfoPyxcb+S7/ko8re1aREsAEw7b2FaaQ10TeiHRCPZDwU0pFkHYzf/vb6b0ejVeuK+aCsg+6117hVzhgrIzwtJMJSQqAwyOZTlotAzpF8R6sE98VFbq21/xL3jfzVmiesjcp400sthDthsWjr58AanVnP8hArRqhnMZ/n/ItWOqz3zixQ1xKQlrvD4j0W4AvXhIXQwQJjRa76IBFWZVqP1yNltnUdk/RglYha/Rok7Hr99eW+iNbfKuoWxSfUun6we9+VBEUBBi/2iw7GhsyJ9l42VkHuM/SNkT2lHj2yZRvOaSsGUAYbW4qSviaTHnslkw5lHYz7+8sD2is53XpNp6uHlFUk6+yM/x4a2vU1zwjQAYNRO2wvslYrI5HwZDEReu4tP7WMDWBrItsuaya34li0wsjuKwOA9H29ssT64JMb1fLjy7mMmtyUstTss9kqFvJhZadk002jz9nvrW6ZrGOhjuHxlFBpEbFD2Qtg9CpDsr8h5oWRdp9ZFytkZylMXnzMyYlfcnzL9KCViFYlEYbTxYWtKGOdvL3oueky2WIeL2hXHmsG5xl6LN5ok2q7UOwXC7uHhxdeAEAAcoAF6gOxbekSbTKEIfgWi1q/d72oH+lJkxadhHJYt8s+F8tkwMJIzdD6LSiDDFg+ewmFat/1aGRnEki/7mzW1XV4991OodEt0C1/nZzTVkZmB9R87gd5yud697VQEj13lsVvHWwWvI5S5ZsqprgmE460MQjR8qm3wKkWWXz58uW6UGA+YfZ7lAzHewAl0Ioae1fwlGc9ISODrXXGncKEV9SxNuO6kcRQqQGJ2D61uKuknPH4IpJfFuroyUPrPnI8Fv+x6+CgO4yzyom1p2B8e886PFw1HmRsYSa8AJkXeC8Lbd12HSpJUlb+yviy/nDiIBbSUthU0EOLZIeKXmidQqYPxozGDOuGHSAS0dDPgs9b+syk5f/8+WrsBCy5+Xzpn48OIs9qtKx6T5P3sjMwX0+erP72yZPlZrM2TwTlewevFRsADXk0yhf3ylxIJdXrhjXBWKxD2EMAGDplzbO+DxQAxq99+FoLTrkGrNx8dDBAgDLBpaubeveS2Ufes2XQXZYitGuL9KCVCIv/sKanp6tyRu4JFoio10l2cdauBbY/LdlkZRjWurofWgwV1t/HU1SZPGb3sJ4FxNdz07ReQP+2uTcyqPxPzharpbkjhur7opYGyXy2h4edlS97c2jKpC6yqPCM3w+NjTZZUI8JrcNGw3ZSW2UaZ1TECcLXskTlHLFxS804e/BiPNuOMM502EN6of4cLdhbxjqdLg9FrRx6NQt0X5qI16yGaJHijowma09lXXGzWVe9kllQzMJj97IEsGWxyQMmUs4YnH0f1tXH9KCViFrX3a5WhUQLZYxQSdlu4eqK16CRhp6FOjC+2fQgbumTsY1Dv5TV1PJsF2brPp5ynnXJWmuM2BGriKLM8MNzvn99W394YGR5ZCYHpZ+xIJYvywrik105vYWMalfI71g+677vGF2Rry5SgvBe1nhYHwztfonGaClbkXXOmOnoqF+6KDawrqmhBVnfpl0HB9tLbcWlkRmJgEBQHh/HguHsjK8hq7WiL9Z3wqsey+KIvva1Nv6V1mQkWK6vfXgXQtsLZIvcIVumB69E1BofOK3r0rK/JNJgoWsWWYXqmPycTNZjCTLdkiVJGW6hHqNR7jxhaCXkoGzm6clxy2AFitfiqm01GDQqOh7X+hOjRf2wbKBp6QWxGE9nbLArqhAoX9xjgNvbWDBv0lOBLaznm8J4W0tkM6bRh1jLOlkpeMw6l1UE2YEu10pvssxcIZ5Ez5u0cpgF07pB9fxhrNmOnnrzWOmzmZLgbFP3tXRY3IqeP7jy3nsv9356jqQ16cU+eJX/Ms/L1MXYMg1KxMfkydLWdWlBJa29KusIeWPWv51Mav0rf2X1jBmPfQS2zzxZ8RfTac7FYblpPBRazlefNFePItelRmwsefXNclk/LPP6L8tB/Uj9Uf977drbs6Ha1qwP5NtuSh4SgXoTrZkosLQAXUsL2otM1+OyhHCm5ke2toMnuDO+L+vdPQaVm4wd/NKPZ8VYsM91UKzVDVLf24v/mc3a5jGj6EnBEK2Bpkwmi752d+OobAuZ0JcugMXeE3DskycczWqdT3kQDUjEZ6NERC6kxWL9YPTqp2QVYqu/E9AEK/ZKp/XP53EJbyj/OrA+4y6zFCxLDms5aTXnY3KYHeZwXVgGquUKsvZZnzU7Po7HieuVsqg/V67rD8erN/zXZVR/t0zrjw4Ol6VQ9Y+llcX8ZVkNVcLk3oJm/D46JgLpbIwR4WpgPS1k0xkWgJdNGZLjyrgUdHZBq8W6u7uuRUaHt7cZGSTouXC0ReC1yAY6Yc0jNovVBAx18hmvtGwYb+Nbih4u6d+1ntFanCt7sfzwLL/IeBu4V6KxyJbn1pp7F0M+vA6g90APXonwYGwpy1kp/Ejueoor5FqmPozshszkltVpVO83S8nNKOAyHV7KlAz6Np12jRp1kGl2Pebz7h1ZMH0mwyOriHvGKSuQF8mVb+92qMQPyqP6YZnXb5bL+oWDRX3/7dv6O1fX9ffmTslUWahKxjmwB2esW7ag8J15Vr+GdD14LIKprBQ43DcKQImeGcV6gFoDGCHkIzdTdlNY7c7Zgc02LZ5lQaSs2ifreqffYTbLwd7eAbm/v+TXxWI9wwV53dbmgWvBcllF/N3XpSEvXaku4hcE+GpFMqvMsHc5PfUbd7Gqs+zdo0DiLdCDVyI8/oj2arTfLAUBmVUsw8NyB7AqsBifVYRP/jYyYhkfR2icB+trGQkFIor7q3X9DHj11dX7yZ4b0bNbG3ItFrW+8cb6fbzYK69lxStlUb9UbusrZbEyf3946sRPsFTLUlYr0+lDUqcCMYgpmjBm1WRcC5osRtNBjQwas5jcQ0wYlBjBVpaSozdftjZBS9AhDh18R7p19Fx7z+qDRIBayn+zuWYHJFAGz70jYVE2RzrjxkIzPF7EXuibDnt1tc4zrHvnm2/W+jf+xnoKX6sSs7+/GiWeccnoDq2WYnfP8RC11vrglQhvzbN9JyyyAh+t5oeTSceTWd5DAb0IiZBp/C3oYKSAa3lgdb22fuedC/ib9W43NzZyCSW9b2aTZ/xZ47SC4OGaYuNE/MRarATqArDPpYBmVqsXVRotaHQQZiGdzG8tZhyN1hWk1toKpcQ1GmQsBivj6kU2R+8n14Gt46NH3UEVNXC7urJTEpkbiVnDVuaN1XY9Qn3YXFu51ladDiANd3fLeTo8XCJjWijClSTXySKp5PTJSsH8ah5jQg3rB4XQytPPXIjJ8Cqf4trd5cq+pdgNSMT9KxFWOXRphGRki74vq56KA93qrzEet5Xixve938izwQuKbjVcZZqlPNMiRVpnpHjzaaEs47Hdc8qrQJsliTJk0JNaeRwcqkVb6O8rZVF/vZzUD8us/qA86ipiGoLkR7O53RRkseAHkz7cIiRCdgXdJMpbx0ho4W9lfUAzzroOMvAa5oYtjheVHx1WsjSsFdBolYyN4gLkhVLLlkLgoS4sbsWy8oFitESYW4WQLN+pRhokisayPI6OOqs7ijLHM/VcR2iEVexGzkV2rSwUKOqSKq9MsZ/xeLVKbgQX3zM9aCUi8qfv7flBjdF92aGBarN9A8OjCpEsxZIhmW+8kasREUH2rDRBFNuUyR4c5fvmAAAgAElEQVSTY+0zT60KOFtbViwsWncWO2O5fSBbDg66AlZ/60QM4PycZnf8cEwG4gVi6YPfC/wbjfw+Gtah602qpS16CIJWNvq6DqC8WBbpJlCvFB54L8snzeJbWmFvPfdZV5NUNBj0KYVAlBljjZlp2JZyx9xF0TzI+goe71lR2VHUOWv3Dr8ynp1BNXTvAilcs6mbBwe5Z8nma6zwXGuFyw3owSoR2T2cgd5b7mvFPelnWogWq/egeQvGT1ThMrMv8U6yFo+lIHgp0BibVU/Gk+fZ/jWZ+7F1ZPK4Fc331t1y+7x4wY1Z3O/X9s7r75bJmjLxo9m8fu960Y3Fsvi8QVuR+fp3sqBStjx1NCkaipcCE8FCLffAfbwIZusdoxbVre9lWawnJ0t/1/7+crElQ2B+rYPm4KDd1SQZm1m42rUQuWhub3l/kCyMiWqW+r3YO1tCLlKY2Duwuiq6AmTG+veEH+6p++hkUUBcmV4C+plWHNGnRA9Wici6rlqg98x9LcSLfef58/W/AV73xox9w1zm+rnTabtx6RWGg9WuD8inT1et+paS24tFV+OlZW9FMjVSFs7O2mKUvHXXsjojs4H2/1y5rv+irE72D8qj+pWD2zqf1w69sBZD1kbQmmCG8cFAzH+eEVSZjpC4v8eEGV8i6+LGOkHKq0+718WCb8yDA1s5m8143rM+bDAXUTtui9lkHnLm0NL3ZCiKtKyhjOh3ZBtjsVjPzHj2jD8juwEzvKd55fw811Qsglz395fpydhDuCdQC6lkMwGcqTXRJxgU/OIV0blHerBKhIU8Mrdpq0Xq8QgC1JkRIqsde+5g8LAnIxjybMke9NrJ8t5iESsyKMkPVIXFhujeM4xYRiLmyWofru/nhQtYxiMzhPB9tvaezGaVajMo/WzWxUzoLI4Py/yTbI+fnC3qR4zhpJDEJPapLGgxTib1siX4JhNhGzXMYpvF24wt7gy4ZjzGn83WD06LmUqx41uiXH9PyCDIEZaPNVZ9T8tveHOTs9K1q8Vae6s3i3b3eLnvVt15zTN4lhXcyhQfr0WzzvtHUKi1vky43dxwd8XeXpuVxC6r2+o904NVImrlBo7+jLmcEOvDqkoyv7hcY8brUBh0YP35ud2ILVNfQhdh64N8W9SnMByTrV7Qoocaw2hj95UZWlG4gFfPRq43FBivsB1iKGSTSgt18Tpby3IH4/Eyi0PWm5Dv8NsnzqHT6nvHQKIMCE+jqrUtzVPCQ9K/pnOg8f+AkCxLT0bDegwwHndCPSIvjoQdNMzqZd89Praf6SE0l5exxRr51VnsCVvjyPcqN4lUErwNp99rsejmAlYFNpt1HwgqC1qE0hllv7RaA3KTetXtvPGyMUEQtuxRdh0e3ns6J6MHrUTUun6Qs2J6GUX88jI+2L3iYdZzrLT/lhLrcr9YWSHY4xEPyjnCvm8p9d6yn9k7yjFaSgQMvKzS5AXYHh52CqOFRoP0WYVqoF79JH3mAe2VMvHmpktH/+/+00X9x1e39SdnCz531qFjZUGwyfCCZKR2nS1SxaC+yL+G73mHkdeE6PS0+zsscvjV9veX/uaobXr0Ht7F6rlbvU6s4luWZZ0VSNlxys3OhJel7XqXlc9cSjfvct0QKxLdf2dn/T7sd+AL735Reeta160BPSesw2k01561gg6mm65pKbU+fvypxkPUWuuDVyJAXrCzl22BK9t4yjowszUZMB7rcGR8mg1mj5AIyzA8Pu4uuC9aUlSZPJPP8sa4WPiVRL3zU2fe3N11ygKToy9f8nvAkPSQ+yj2AfKKjVO3Nnjxoj3VuC4WuQWRUKjlXoBfKBvIxWBqSR7Te4eRxRQZeMyy4K2Kka15/xiLvlcmPoQJIYbUbEOJ0ALFQnz0Okb3RfT0puPL8GtreetMdlEf159+fzbXXk8XKL7efWUDnygNFNHrLcFuG9CgRFQbrdXGwMVFf96y5Ia07D2+8ApfYbynp91BGBVK0jIjE48TGUB9i8NZc20ZqHqMMsWcofCZMtYy5V+/x9OnsXvKK3lwe7ueXfKtb+XWnF1XV34qP6V33skzZqRNswPCg7C8PFmPqayqndbYrYDE7PXGG/y9rTGi5wEs4qigCGNGrREzIaR/0yc3/ODAbhXOYH/mW4cAzBzcT58uNd3pdHNfP7v299usFd2AzVqjDOxs/W1nZ4m2YP2km0XfGwoE0A1rH2hXjdWYjV1D74xPR4nwApMlRfA441svC0HL6xcvbB6dz7sDhAUtHxx01jJktZYXFtrs1alhc9SnEBuTZ1G7c6umjY5DiwzdWu30UKmUeXLBQgmwv3GPFiQC/BUlD7CrVwD27e0arLFWJTOCTTxfnYVEWBA502jZPXUUPCZNH0qw9PoWX8FCs/mQAXo68rnW7r8vX3ZjYkFIrNgTY3zG9Pv768zXasVAcMhW4VFktpcfrX9j9W1pLdQkL1TPQ6Eya72ySsRkshr7otcF/76+3l5Le4yRZYBEHXll9Uo2zru7NgXqnvtnDEpEbSsjz+K0LEX75saWG5bLmPHGeGx37cXf2b6RVmuz9apoG65YyHqG9kbP0khkFj2KXDdXV/6YPYNYK4QstjEqvNWyptG7mut7d8cLV+1NVxnTysLwshIsS6cFtVgsumfIl97d7VIpUd/89HSpJTMt1NrEv/RL8WR/8Yvrn02n6yl7OubECtqUBwRDNixXEWNW1qwrw0A4iHQBqUwMgufXlP43wOZeLnSr4EAXUXmws99/9at2+2MoHrDWJSLALDf8m6XibnJZvO41nLMKRUU1P6JLBzRvkQYlonJ35XxuI7TgAyj4b721/nuJZGRdrZaRYR0oh05HafxOBjlrV2cr6TTnVlSm5bksBbYlRdKaYzkWL3Bf8gHkbpSOjbiKq6tVZceT++xvMGC8Ilu6lLnlgai11u9f39I00Z8r1/U3jm99zSwKVGM+pj6BN4uFLcBZfQGpkWKx2dhZTQf8bTzuXD0ZRtblms/P7d+xuICM1sdiOhBshXuensZMC42bIUtRLIG3UaFA4N2sICgLbQKy8OQJh+MPD1dLnmOe2Pvu7nKegLXE3DSZ6pjbVCI0j+rNmi0UlVHEdnd9F8c9ohEPXomwhLynjOvfW3C193v2O8/3rj/b3+/kY58eM3g3zyiK0vYlMjqbrQdQ60s3xssQlDVLVvRBInBAZw0kZN5E7h/vIPfi/ebzpZHN+hhZZ4Zcw2gevndt15rQPb1+++Sy69/h5ThHmyXS3hhZqTa4dPQ6Cy7KQnsS1urrp7N6PYBpPOvcSk20qrhhk+PQZrUo2BwzGCyqVvfee1w4eEysy2d7/lPcj1W+ZH01Fgsbhn38uM09lCkp3ReN0HO6u7taRt6Ki8A74x1OT9frobB3AVIm3x2IHrMq77Gb54NXIqyUR4b+ZBEF6/eamIuMuUqsPjZ9XcBeFc7IqrXewXPVZqoLW4qLhzjAMLKaCLI5lvI1e3ZECmXmINdGHFAhuD2ZcpIJMM0gMotFrb8y5rUmENch40v+0GSxRCgy2lbmQI8K4URKRMZi0/CVZbHLzdnXT+f1U0CwHHt/y3qYzdqyUdiz9Ryzgx9MZykSBwfLNFhsrKizJPKgs9kAWdfNfO53O8X7Zt1D2w7wRJU+WAHRmln53nBtPH68+jekHnuCgKVks8DLrFXcgx60EmGtDauGax2umQPEI3R4xN5nJfaZLNjb6x8DZFXhzFj3mfmTaCfrCaEPTU9xseb3+Hgpd72gePlMfUBnlbCohku2oCPGgeKLOGsshc1yeckA0yz/XV7W+hOjRf1Suf2k2qW37qWIOfWKi3gPtKxEa5E8mP7b3+YClt3Hy8lnEKGXMw2BwD7XMNF4vJw0K20yg+zg+9bfYAVYz7YYQy5qplqd3NBRHYNsk6xa80Gk0odoPdMKANUBsdMpt9DhLrJSJ71CUFKJiRRRlEVnm9VzjcE3agUgW5C3TDljLsct0oNWIixrlHXv9Ayr1m6PICvGRx+MDJVkAX/TqZ/Nh+B2qwEWK07X2i8C7cGZgcDkasYtqA1MJgtaFe3FwnaX64splVIxWSz8ehVszZkCqN1M4eFO5kcruNq9LAsD4rtW8Ocnrg5L44oYPvIB1bqqRVvKyje+0abd9nWnMFfC8+dcKUHQkwyUYxZhH798KbW+9pqvCCHmAQVa9FpYm5PVpYiKkVm1HyzlKhKClubbCq1KHtCKgy77m1EE2IbzECcIx2yr4fl82URIxrh4/CAtMYtHZc8UtrYth1IPetBKhGeNSgXPkkmTyfLgRyr2O+/wrJw+sTLyULEUWH14sANhNqv1V391Vda0lGJu6RdhyfYW1Niy4o+P235jrTlcOVkkR1cn1sofc0MxF040B8zNxPqDaGVDKx5MljI0SPIok7ErCAzzvTF4xxJmbCA6cpQFUE6ncTc09kKe1s+UG4+ZW+FG3N+Cr7HIEBqWAMIiMh8nAvO0Rt065gi5gaCT9TAmk07QeXUjosJOTPPNRDrLCy3VvdK5kdJ2emqPazLxqwhiPjNIhOZF/DebaTEed/xqHVi6nsQm8HgjPWglolYfqYXrtNVtCr7V2VVR3I83hhZrMzNWKxZK7yGvujEO5CimquV9MTZm1HnyJbNHItTa2rtRnAILeGdKTTQHzBhjdSqsmJYMyiHfI4pzW5tTD1mwggUtYWZZb7DMpBBnATdQCiwlxdowlptBTiBj5qx7Ro+HaeuAr71AIiAdLW4HzXgtLiVvc+Cg1ZBrlC4aWcFMeLX4GLVLxxImXpdbS7BdX6/HUOzucmHXN66m9bq+9oNqwV8ecnYP9OCViCwaYaW9t1yw9j2o2hsDszw9d5h3XzQRY8bCYhFXN5YHFlwk3iHess/0wW21HpBzlHG5t+xzGZMiiSkCLOCdIa1WTyDZH4Uh0BlEPDK4vOQAKLvgGUu24scfzef1hwef67I4PGWBWeLwd52d8YEiR/7qivutZGSq5QuzipF4BzI2mnSvsN+3dhLV2nq2FXspS2HRp+y2HFO2QMxiwdt3W+8mFSJvTFFQLciy6Nh8sUZnnoBombNa/e5+XnoWYiv6HhajUa0///P2s6N3mUy6DBuLn+6BHrwSUWu3/l5WDPahtTbZCzEJiNWR1WHnc57JxIL6MhkUmQZdlqFgKUxR6e0ouBHWM35r7TP5zlE7BEt50bLTk8VMznsprpYs1UYfe2fwGQ59+azsvZmycXDgr7eHcuvLlPmLRf3hZPXHP5w4yoIFk3sVvIAuWH7oDNzNKkeenMTpfU+eLDeWLk7CijZpK5rB+wiok4IkG1jpbTbr0gGnLUoEiClLXvSwZHTP6o98auyAhFuEbYJsYznZEA2pkZbAAUXd/RhJpK4vMgFLkwVZZat/otEc46d7oEGJqL7l/dZbS9nB6iF4lSQz1+lpxxtnZzwAWubxY6wZd5cle7yaA97v5PfCQDxFur7KyclSTnnvbPnq8R6np/maDdZ7yb9nZW3GtYQsm2jt+9ybvYuFROj018wZhqwzPR/fv76tPyirP/5BeVR/58pQFtCK2/KxsA5j0aHZUvY5ayn3vQAhyYho9j2ZtZBVChjsF6WuWr/L5mt7lBE8UXwFvs/GlcmVjzaB90zpe2Xf0xbQYpGPlmZkZVOAH3A/tmFlzrVUiDdxm7BDYkv04JUIyc+y5wTcsd66oBCRVQNAw8TsQr8WS/5o3raaAWqhf3fX9RSChe29j1TEM4Ht1uHOFHpP9kSIhqWslNK9C4vX8J4nZfFslm90xxQMT+nINJPEnHooipfUwDK4srGPkRyyOm3/7StetOpvXy3q//70nPfjwEJfXKxvBKTaYPN4Eej4fotCEBVW+rQvuVCZADmLKY6P7TK1Hly46UHSEhdiQZkt1eOiin0asdrbW4d3s3ELbG70Qe5BlIyk4qI35d2drXBBADJBgDFlW4d7RXS2RA9aibAsuozrSfO4Xm+v+mpW9jHl2Cs8BaH/ta+t/v3xY/99dNVCPScM3rYq9GpXdFRDQcdWyHduiSmTKIn3PKBOr7/OD0pNrcach56wdbYQRv1c3fMJsgmuMS13Itkr5eyzZ6tFu7ShCz6/vq71m2W9aNXVVa1/Znpbf1BWNb4fHYmJz6TBWZXVSllmCFiujv399c+jEs+fxYUD8913+d/PzuzFywQ7ZTdCX8pCdlbzNatfxJtvdo3MpJYv0RvPv6hTbNn3M1HNzFWBe3npTtH8tFocEZokx+ShUgcHvA/HlulBKxHWPmP1Eqw1YntSrntrrxSr/4o13lJybbg9xZXVHZDyWJd+XizsM+Gdd+IAboaCRjUlMj0uUJfFe57VjyLrEoqMOQ890ZdlaFlG03Tajb8FkbXkmS54JQNkGY8h9mQ8rvWVsixaNR53svePHq2jFD+czOsHd4vlxPSBYvf2OuUCDKU1ZLkw2m8eBTHKjYPn4N/oRQA/ekvqYbToXslsy+ceWdIsDqTPxsPnVu2LTf1+0Xvs7KzGprAUsZYxSOsu4j8m6CwXjYdcZCwOPOP62i7p3uJCevkyJ9TugR60EmGtUZ/MCe+eHs9avWusA0DfG4WDomcx4w3GHZsXhjxL+DxbqInJdiujSgbV93X9vXhho66eMcxcQn2MOWvsx8fdgS3PLdYAc7HojNHWjs+lrMaSAKlgKaAYH1NG5nMbSQEQoN0oeGeNUvzF6eUnBuUHdz0W1asWqDeiFTxi+cFHoyWkzKDH6XTZQdTr547NYU1oy+X53D1LGla0dah5Kasa6jo/t5m0T4wFE2Tw//Zp/MP6a1jPstKQPIsK/mWpwDD3WqbUuzzE5di0D52tZ4QmsXfVFUzv0YUh6UErEXre2X6Rjee0xc8q77J1h/EBwXt8vOwAyg5YHYj4/Pl6dUxZ1j4jm2X6vYbHM+/AZHBmz6NInmU8MNQjqgyMejfWGHR2Hv7fyirE2utDt69b2XLRRPfT/Nh6IXWe8cN8njvjHj2yFUSppFjI0RcO1ktr4/k3L5wgS+uBme/++T9vH6BHRzz6eXd3+RsrtRBxGkxQsH4J0+l6ee4/8SeWPvEIlnz6tC0tCBObsXgja8Tb1JZl1cfSxbr0USCssemD2YNAEdHdR0v33t078KPaIfpCxLUlMFhVzm2sTU96sEoEWx+NLOiDSAvhLAQ+mawqEV62mGeFv/oqP5y0wfGzP7v6O9nHJYMCZpEA3S/GksNSGc8gDl4KOMoMwGJn37m4WL6LVsisMVqIUEu9Hj2HGbesNCw2NWS99PQoBVTLWauehTa+WJaj9Zz5vEMkvn99W//pN1+uB2LiatWQcfPW4j9gRG/iWTAn0g4zBUNK6RSLLKTulRLXlo0OlMkUkbEY0bv292t9++1cRbVoU/SFGK3LCtYcjXiVtj5ps3ojWXDqJrC2vGQUO4uW1vfLVru7J3qwSkQrVG19n6XC6XXP+PM9CD3zO8gN8FhrGW5N8h0so+H6ukN8vfcDqmYhDuzAOTiwUWj5zqzKYindmPCuTLbIfz95YlcnlsGYran2kjy3rEQuM4e8F//i/c1zU5Syfna1xHvJ8+zZM/sZstLmHz1a1N8rhHF03m7U/MuazAyCgc0bbThttVoHl6fFAUqUEf/Zzc2YiQkcK4aA3aP1YGPj1WPclvIi8+iRhgXFySoullnvTWG/PqW8MwV7orHKeWVzuL+/vvnhGttUeCXowSoRrVA1+37GPZepDyKDKVv2d8YtV8p6OntLpgEOPytlOiMXLCjdQhyACMGlzZAAy4DEmlip548eda4kWUunr9vCmzP8VlcKtpqsZZAI2U6hVfZdXtrnMevfw8YeGfoRQq35oIuhmNXfn+23BehEG2KxiGMpUBY1s+GyMJWl1ZayCo8BkvPeq6UZjDd+xsiXl5u1xZYlVq34g775xfqaTpe+XwsajHKqoXxo/rq7Wz98kSH06FHsv7ZcRYBbrc0KdAsWWqbSoVQoMnOIrq4tAr8nPVglotZ2qFqjiZmW7dk1l510s/VxMm656PdeLQL27iylMBor3Djsc11IkMUDsb2a6U7d4sbVWRtWp2lvTFqOfuMb6+OaTrtAat1Js9b1mDZ5oWAdnpOJN5xO1xFvy4VnGSxZt0x2LPp3r5RF/dPj23pxurD5UG9UK0UFi7tY+N3aNJNlyqJagkJbiZYmxUqAejn/WS02WoyspYErUi4OD7ugGRlAZB2WzDWDd9ZBqV4zKpZ5EtVayKy7By9HGRlWkKmMxfHGcXq6TI9im1nOq35GphANqwrb1zIK6EErEbW2oz0ewmAZD0wGWrJD8o8uY4+YCC/LoQWhm0z4YWaRZZlmDvQIcbAyyqw1iBQXGdOkswnY/VqQCCt1u6+bVcqLoyNbjssKl1ENjclk6dZhY7cCebMIVcu7jsfdWCLj2+VDZpHpDfLkyargRTGrw0O/utjtrT2ZESysYxHYxDx96k+m9EP2Cb5pQSI8pQNFcjz4nZVGjQJg0YlVd1FFnnGUBcPeJesWYuP3GhhJl5gXwMR+1xr/YAV3WoqZHFvkvvkU4yQevBLRl7yDx0K5WBCaxQu4ly5jz+6N79zcbBb03OrOke/rGSLn5+sN97KIAxtHJrhaI85eQ8GW+BhrHrJl7a39nkUWGPKBasiTyXJs87n9vtG5J/nAWhOr5pO+dnaWRQThso/qmqQMpqwmg8Xxbmjl/gJyszYzsxQlw8HijN4jGxBpkQ5gQgxBi6URacMHB3YhEa8Xir4A8Vmaa2RlA1rrq7Ejyl2nfWYqXEYKRrbAkHcdHNixOtnA0EgJ2TINSsQGtKlV5/FCtnOrhuGZfGipoMgCRWuND1oWRHx7u0Tr4K6xjEErUI99J1LCkaqbRRhakAgPAe0r1yA7MuujeUKeO1aRQE9utGSmaV5mLmW8y95ed7H3Yq5Ai6+aBt73Zre33LpG4xwZwOIxobYiIl+hVashS5YC4nUbXSzWJ388Xv2u3sxPn65CkKykqec+0tfNzfp8I2gxCpIEqsG+o3Posz5ha50sf/e2kAhrPBntXruF8P+Sh3Q9gCEm4g8mtVh1jDz/dtS5NVNJuJSlcZL57mhkB4pG76YNqSjC37s3vtuatQcZVWsbwpCNj/HmAfdolRuoIxJ9z+q1AWrNOPLeJxtPAndRS9r9o0ednEfac4ZH1gZ9dZWbNH0zCdt5G9fqaOZtJK/fOuv6ye5v+dw0WfeX6AjTxrNMIhWhiKlHo7ZGZ2+/zRVAwIWRsGLMxjInNFy2t7f+Ll4AIwqRWVYPC+bChmB84zVJwgZn8SOsJ4BeI60ESQWC/XaLNCgRH1NfJBG/RSfOPm6o62tuQUa/u7jgvKg7jUoezgp6Jn+fPl39uxd8uFjkaw1k3DpM9h0e1vrlL9tj8lwPbJ2zPGDJD9xDu26iS2ZdWEG7pdjJC5sosXgfrUC1uni8NdQXigKCHxED4rlgVgbbpx14reuwHfw/2g0BVKC174YM8vH8e9YEy3FFPj3L5WBtogxMzyiL+Mzn6/m9X/86/y5DIvT7ZzXryMqGcEY+OhO02i314kUu2tsqHAQhoDcVNivL4mENimq1A9E8Yve/J1dGrbUOSkRtDyzTv8125mUEHrf2tXewWUgEg5iPjrrnoP5CtnohDo0sqgC6vuYGg7SmM1YsIHzPYr66Wo3bYmsrO5l6QZYeScU/Kjx2dcXfh807UiytZn2WIcH4tjXjSL5bVAjMW+9N3NSRHF15SIZxp9P1BjQebIeDZDpdHl74d8sLoG11dPBmoG+rh0bm/pEgamGSltgTlgprWR4y3YsJngzSJCvPRRYAnod3wf9nc6Z1JcKMlu2NKVIOsCEzFQ7lb956y56rewiqrLXWB69E9LXeauX1E3AxBVnzlDwEEEiO34/HcV2Hy8u8DNGVIxEc7e1TqchErb/lu3nyV6aGZgxKrXRI2Zete3F31ykZWrlCqQDGExY6CGRR84yUZ9776c90B1aPX+TnfRVPizyFxENTpeKhAz1bzjjIYCsmp9ba/SFbdlP72d5+2/7+4SFnDmbRWZCefCaLO9AHUgRXeY24+gTgROVGrc/AHH0XFNoxi9GwBAXgwkhRwsEeWYFM+ZxMllp7RiGbTtfnr+WAt9bSi8XI9OyQv8m2at4yPXgloo8fuVY/lmF/f90QYi7MVjmg5VSLe8JyiWUCu62MIvClVobY83Wtl+vr9nHLQ6vFZ28ZPExWM3mUScuGnJbzxn6HYlhWNdNIDnnyRSsyWfIUactg0ueKDGZFCnSrN8Ar3vbJQD2mZ/4QCelYv/NKsrLgNAuuluOMDt3o72hJazEn0nFaJtnzi3saY1+YiSlz0vdm5X1bUdG6YyGESiQIrBz01kwPHXwauTz6UDQeJiAy7zDERPzBQiJa15l9P9tbSF7SmMgaZShcFs2Bl2Vmve/5eY5/9/fXD2tLiZA1EuS+ZIHsbN1a6uqUsjouixesM8bKPsD6M9kla9lkY2ikGyV6n6zrVK6zFW9ioR3MnaP5vkU2w72m55lWGf5Ye/molPXeG9ofEg0CMRGsjbJkDrkAOviOfd7H3WBNihfLgAliLdBZtoQl2LwN3vd9rCBBbGBd4wPr8d57y99oDbZP3wiPBzSSgfljY5PpctZaZLR3D16E9s0UTC9HPSqtHaUZb0gPXomotS0yH+vsxUTp31tCutXlKvd1i3u4NXPMmyNtqGTkC3OlMFfQaMTjntihlcloicam3Rns+wcHNooxGvEGkV7KJxpAYi4jOS9lr1XQj43PU4SzqNjrr3P5bDXZOjhYVYA81KSUZXdab08x2fkb54v6H47O6r8s++uDk5qR1STr7beX2RlWVsFoZPuzZNYDg662ESCimTSCTPXhxOBDC2KNApj6vA+UiMWiQ1VaCti8eLEqcCaTZW54pkaFZP5ICCCORVtSuuLbaLTUaNUsKQkAACAASURBVK174l4WZTJqmEAppVOupJWHjRNB2p9CS/BBifiYIj+yrmPAekkwBBL3Zgo0DhO29rMZD5CUCm+Lq1KihMyY6qtER5UTS+n2P5O3iGnA75mcefSo1jfe4O+j97mOp4tkn97zFhLRmtViNXm03rEUO4Ymkt2zmY9osPVm7/itb+XeLUIimLEeVRDO8BG+j/G/Uhb1w0JuqiPtPX+RN8FSw7T8WbOZ31dj07asuHB4tUCmme8DLrPGKYOerIAkBMBYAUB9e9szZrB6DXjVPqNNxBCExYJvVImIRFBcZj0wx5n5uLhYDw7N8lcErW9IgxKRILb+aC4n94un8HnBwdjHssOvhVBJaw8C+r33coq+9jm3NuTKvJN01UKGWPJ8Oq31/ff9wyObSSLnR7dJ90puyzWWin1Lfx99tbparVgGZvAgeUBnjrHzghVUZPfEWkVjlDzCYiIkP+kSBR7ap/nISg2+uFhVSLoGXvP6g/Ko/v7UgFSQLsge7FmpqBzIrFLv0ujAyYnP4JlypWdnq4pJNr2ITbpk9GhjSc3Nc+dAEPXpVultfPa5DiqS7h7LGsI8eI2uJLGce81T2XthbC050OyK0mKzPHkPNCgRgjwXJ1t/zUeRwsfaZut9GhlJOPyibIE+l+cyzcRJwCXdgmDKUs3ykun6fd3L6Cp9d+fHwVkoo1z/7PxmDNiWeWfKAfoOyXgBfV5Y8WYsriLin8PD7hzT8Qk4O66u7AKB2q2f4SOc+/pe+/vrPPVKWdQvldv6WzcGzOylfESa3nzOu6i1LqYFs2ByIr8PYCo0HtPxEhYhLQkQqXQRZN5FVuiMWotni3+V0ill0Ditd7bupdczijHA51YqnV6vTRAkjXJJq2QTBWJvbzNBOCAR969ESFRPIwUtlqin8FnZHLINOPuNLrh2ft5uGWcvNn5LhnguWi9zJXNJ19Cm7mVpQWcPMYb6Zl26e3ux8snGZhEzJq01ke8XrY+85/GxLze9rIno/MN6WjLMihdCo8iM7P0k5q0P5A/tsi+TybbOWgOVC6InXQcqwVpt2TgoV83QAV346dmztndEYZloPplPNYK1ZKzF7S2vJeG5kLTmbHXSjCC4UjpfqVQ0+gouGUgKC6+Vpw4PbRfQfN6u3HjBmFukB69EgN88AZV167VYlHq/Wmut20PrehKZcQL9jA5CdnhaMsSzkq13RddQ9ly556QCJ9doE2XeWhvrENPKVIviJoP6LTTp/DzfuVSeRda8M5TAk/9ScUbGIIsxYSXTEfPR0irAK3vA+BZ74rXX4nuvpMBno6R1kNPJSdzBkl1If9IBcjgMAJ8glckLQOqjMU8m6/5Jy8+e9b9LpooyH/pY7cxa0bUkLA1cBkJmBZAnmMBoT57ECgSEFPPLYtx9LDwEyOH9mWvo0aOlwpst955ti7whPWglIrNnvWqKlrtVy4pshpQW8lHrZM2HrHjUdLqKZlqKBkNHo4BwJq+td4WibjWJsirSyvmwevzM5+vGTEZu4b5sTlhW1Pl5zj1+dbX8jWWAZlBiRtb8MqODuTg8ZWQ04jWX2Dsi9iSrYMs50fPvKbeWvNSl3VdKsBuHNT7+4M44gLJNm5gfM6NRZXL1sWjbCsqUF5totEnHISrjLawytTKlpk8cRKbwkecvtTYCUof07wBVZWqGROO+u7MVVUuYRPdEhL2XLiWtN3YwaETsntEHSQ9aicgc7hZPyAwm2aeFBbNZfl+mbEpeb9mfMHR0WWtY9bB82fvMZlzIs3FbAYleLIdO388qH9roYQf4ZLK0cr/9bXt+PJTIWmMm8zOI5y//cvscZd2W2SwG/WzNl8fHbU2zWi7Wu0UrqRhXVJjw6Ihn27HvIh6HITxSafsz09v6e3NDE5MV11gK0Ghk571GwmR3119kTIpVStZK/8teOKyYVimFjnWQldLFiMgSq1Ffd3Zl0g5hNaAUOZjbE6qwRizmwH37Bjl6KbW12kWtSuk2m0SLouAlfC7XQz6PFbuyXGn3TA9aicggEcfHfudcvZb6glDXdRZYemfWoIHSeXCwrM6r0Vm2t71Dw4rTYlH4UR2NiP/ld6ODFYeBV+Hy5sauF+S5iiBPrHmxDKZozfV8ZpCpbJVUyFGMjz1X32fTuBJ578z3RiN+0Ou9YKVLe/J0Nqv1F36Bf/f5cy5XtWufpocyxrPqErA0QyvvVV+WXycqCHJ4uF4EiWlr1vXqq0tmkGVfEXnMNP++/sNXX40tck9rbhWq0hqxBIWc94wlwKJ7vTF7m2w0Wu0GKgWCVZEO1iCEvExzOznxG/j0hTl70oNWImr1ES69Jhoyzghn3cQKiOF02lnOuqRwJhMAcUey9k1LLZeWfc32m2xWqA2Zz31utdHVaLRM+fS62S4WqxWGYRBKy5mNeW/PNoYODrq6Ql5jLk9OsqBXjBeNvzw5rg9AKHx9kAgLzWLP1e+bdad5RuVs1qUSZ+POptN15czqqySz9pAizJBiuIRbA/qZkoj00H9ZDtYrX8oiG2zSrdxuzxLFZUF+kQKyuxsLht1dOxpVCzM8DznD+t6ZvF+PWaL3kZ31Mmlp8kL6rRYgtdpKxNVV973T01V0g11gvGx8DTYZG/fenp1Lb627jPC3LpbWZlW5CzvbbUYPXomodcmHP/uzq3MP5V1+Rwr629vY5SBdWYwvkCaOw9VrNijl1qYuUyZwtTXsZVk8ebK6L1rkDVIvJcQO2QxlgwX59XlPXTcCa5m1zKWCxxR8L46KFdMrpdbHj1czv6wunZKYIoB30/zWF4lgFTghzyAHcR/8/4sXdl0HpixYGUpXV8u4Mh1ICqXN4/knT9rd86+URf25cl0/LI7FiUVHgCRjzJagOgb5WZ0XGTNH38FEakXi6KgtDXMT10nGF4sqlLC2pRWVbbLGDnWvtTHTksGUskiPB5laZD33/fdti8HS7p8/75fOCd8u++09Vq4clIiPyeIBT4HzhLOuQBil+0m+ygj8rD/bKqx2dcUzs1oMgk2uVoEPd/Umz8RBbRmMX/7yEglh88hkAWv0iItZ4/Jvz5753YCxDhbibI3JcsFYiBvjD5Tn9tBu7A0rWFYW7orQMok6sUw9r7EblLAMv7Lv/MXZZVesyioiEkXTegNgh7FcpJZo/oymblW3LMV/D0CGjx61FddiVwaJYO+CzppZwcOY/fa2TVCgScym8QNMcM9mPFZGIl16niaT/oWl4Ge3fhvBnT1pUCI+posLPu9vv23P+91dpzTqplFWDIBnBHgIKrtYnAbbtzL+QheuY6W7Pb/9Z3llEL7owsFnybfZbJlpphW+g4N1xQdp3dZ+Pj1tQ2j0HtfIh47JurzsPpP3WMlSUASF5J132saTCXqVxbykQYf5vLrK8xNCDFrWG0qLd/4hgFiv/2z2ccbG7W394G6x3LsZN4NkLs008zm3ftFJb7FoC0yUG9kqM91HOZG/Pz7OKRF7e1ygweLtm2WC6HT2PBaLwlJFW57X2iLbQiYsH6Wlgd/c8HbwEHRRupm1Ca6vu0PJetd7qFw5KBEfk8V7rKdBrevC+/HjOC3X29cMQYVA1nJGdsDVMUVWxgdzHXpQeGvdFVnu2qoK23Kx9Fk5L33uj9LJ1uHkKXJMifGQhv397u+/+Iv58cn6FJ5MimpGZGTi48fxeLz50C52BElKNxd4otXldXTUKe8tcX1wB7MzS+9hK1gYxQoRwPm3TpLQOh6S3TCwuL1oYX09fbpkDOtFpU8sgj6jjZdZJPa+MjdaZptk0QGURtVjz3Tcw3u3KC4tLbI1s6MpGBPcDFLDJsoILwTPyc8yGyiq0HYPsRFbVyJKKX+ulPJbpZTfLqUck79/vpTyv5RS/o9Syt8vpfx8dM9Pq+y1Vgz0mkr4tu/6IHgQewK8pZUUmelgxXH1TR30KrvKNGjcC4WsZMCbrFqL4GHp329RQmQgJSvzr33jzBUjZaCFyM7ndgaYniuvUiQ+yxoLf/pPt8s0qwiWDPTsm+UBXsm2TmDzgayHFnmN8ynjUml1d8EIs1zMGhVkaITmqZ8YLepHo4ZKc1mfCgIZrWhhfWl/dqZC2n37Iy1LgQmcTMAprpZIcWZZtyAwLS2yvfn0hDLo7q4tzoQppUyxaLlY6tYWaKtKRCllr5Tyj0opf7SUMiml/J+llD+uvvNfl1J+7eP//+OllP87uu+n2YDr7q6zgpigQ20Iy/VxcbG8D+MleRDK/7ZkDbGmc/L76Pdj9ejx9gIqEeq/owy1HC8UEa8NdbbexXe+swp9a2VMZ35YijziinS2Ryb7RVatza4hu4+FMr//fq1/9s+ufv6Vr/BxILiQ3V+X8e6LRNS6ni2EyshWMDreHQHurWeUbHsgkbRNXfClLN0nmWZr7ExjfPxKWdQf7SWUCOnDtKpesoG1wGnSimmxFqT7Q1oBp6dtsQOwfPB7S4vXWqynreJza9Ng7FaTMu2KyCpO8DVabgn2eeTfZSlrkrLBs/LdNNycVVKt68chJqKU8jOllGvx718vpfy6+s5fL6W8Jb7/v0X3/TSVCKCFXmxKVM+ERfH3Sd313BOaWA0BZtF7e8Gz5mQAdbRXtb/cm09cEtmQ89NiUDEFK4PW9MmAsrIlPAVHy2zru1BoovTjqLGYR/LeCKJk86Vpk74tWoZ5yDwuuIUy625VZAWCAw8Cex773ZfKbf1X44RLYG9v6QdBrXD94qxfe+slNd1M+iEmmNUnwD36pFV5FcLAmHiu9d3j46U2zoKQpMZpaezaFcE2JbJSzs66HGWrIqCcU9aJLxJEBwfLzah/36cnB96NrZlWDK1xeR1st0jbViL+g1LKfyP+/SullP9CfecnSin/oJTyT0opv1NK+anovp+WEqGjwdn+wgFpBbRZRkJL3RI5lkgQW8/UfCT52hLaqHoZ1XmJ+hlYdSRaoW/IwAyC15LBZMlfCwlhZM35Jo3H2DovFjxOaj7vnsXabkeKgDX2qL1DFBw8my0bTcoaIZ6LKioeaAXUjkZxO3R9H/AV+/uXv7y+318pi/q7pceCoqZDywBbGSNaaAbDWcyAkrtZ/5bH/M+erftf9aSzsrcesgKIFb4wmROtGSpCaFoCIEtZzRH3hJiVkQIfb0b4yVQjj6SgijrERsJgC7RtJeIJUSL+c/Wd/6iU8ubH//8zpZS7UsouuddfKqV8t5Ty3c9//vP3NgEy9kevBWs+BGvdgt8tCzWLKGBMjJ+tqpItmRTzOe9ujKZ919ebw8snJxx5WSxq/ZN/Mn+ft97K7b2XL9fjJqJ9o7/LGglGJItjbTJf7PKywKx1lS4kD/GyYu729lZ/q1PmvVi9/f2Od2RZBWQGsYJkqGoZKYjHx7ymhpaN28gmYsjQr5bztWJUa8Wp2IXiRnICM+miWcaIGNNiEG9D6IqY3rMZimEx6mgUoyZWRT/N0JIpPcjXepYVSJQpW44WyqzBzCaturE+Z2fxYc/mgz3XKy28Zfos3Bm/WUr5SfHvf1xK+Te9+94XEqFdAOzSsTC7u76AziIRXmyDpYgwuWQ907pY1V7sg0z8QmYvWI30oHhl78UUbCtgEgcNnov/9/YRlAArw+LmxlZGZMVLll7LXBvSzZsp9wwDjP1d/9YqVmchV1nERJfvtvgMWWsewtHHEPdKp0d7YDzejoL3q+W8/m6Z1n/Bqltal1Xe+r33+Pdx0OqXZ1ZMpAxY1b8s5SMLEyKrpNZ2iB6ZDFYKm06NiYJ+rOIkXlyCxSgeEqGZnNV18IKY5EYCMmR1rrOsRG/sXu57xCtbom0rEaOPlYI/IgIr/131nb9ZSvmLH///v1NK+aellB3vvvehRGwDXbTWCPsBygMU5JYeFHpscEtY1phOy8YhyrrWMmsyco1milvhXaOsAS8LBtfeHq/VwFwprHIjWyPpIvaKRMk5YQpjlndkZWEG5+t52N1dD5y0an8w9xhzP8sKwZJaYhvkHGo+g6IE94oV/xY12mLnpb5H5GZiGSR9miqyz18pi/pauag/KGTz6Nrno5Gv7Wjtcne308BY9TdoxxrGt8iCi1g9hGzAkrwmE7tMqXdBScpuKIuh0VciU3I3yyga9fDgNg9S9iLJoahoge1tNra29zEfG9J9pHj+fCnl//o4S+M//vizv1pKefzx///xUsr/+rGC8fdKKa9G97wPJWIb8Ke1RixeIuOuk6T5nAnD0WjdXaDhfCZYmYLC9o20AiM3hy5nb72rdB+9+66tkLNxeoXwrLHJzqh9WwFoGcDS2HGIWvJbH4CWIoIaIB6PSndRxu1uGTjSHeMhIyzgviX9H0UBvbNKV0Fm32EZNHpOdRwhGx9iNywZjuwT1JcA34SNu3DJok/W5gYzS6vbqv6WjW/wGEtnI2RTp+7rksLPOhwZ07Ra3jpmgv2//v7JCRcobJPoZ2Zz+GvNR85Lwc4UTeS9R2O7J3qwxabuC4mw4HpWsc9DGDFG69Bi/G3tDf1ZRrGAISCteC8jTc/F5eV6R0Xdh4a586Tb5tmz1b89edKu+GGPbdprBGikVYIZSoYVaK7XOcqSseLEpBuMrbWF8ljyRKNZ1rux32bT//F7D4HSzdZaEVqGhltuQansIl6PNfzSivjhYa3/ye5J7NKQmQXWYmWCOlp8VHoyJHqB3N1MdLW89va2k3/LrqzVoYXV8TFXfJiGqSPlZeWzFhi4lG4e4I/E+DKIigehWd+XflQdA6H96zKQSRfbiXyAW6IHq0TUyosqzeer5YXBe1rJG4148KtVQ+LszPYXR5T1YaNaYKapU6RYsHgkS+6w72cCAiUsLg8TC1HMFtPTv8lmeGzSc0gGi2dkvmUll8IR0kyWlqcYW6iZNs6iQoj4TbbQFGS7h7wwtz8MOv195p5ZLGwDLULEIhc6CGUV/tBksd6wS19I+dT1yvsEU1kFqU5O7MHKhWWT4LW9lZUYvcps27iYK4ExOt7FUn5aoD5vU9ZqF5LJPNPz41pMpv2DEAr4rLVhEKy/1g5/G9CDViJq5S6AWlczL6y9hFL2UjZ41SyZH17zssVrGR8+u7zW29ZcsL9Z74XMCE0Zd9HhYZe+CEsws2day1175ZDltbNju3Siwkq6WGDm4L+7s99FH3SZbJNozpnMlC7g6bQ7O/QcWO+WTbtFzJnVj+TszJa7VuyenlOrerTMFmGVR5krkM2xjh9BG/EflEf1wzKvHz59wTViT9BbcIocrFcQyovMzjKFvBC4Iu95e9svZ7llk8q5iIST5X9iFnf03pZWnY38ttwODDqEn47Vn8Azt5UbbqFXpdybIvHglQhGWshY/UyYC+rurtY/9adWP9/ZsWORmNVp1UCBjJpO8/tUxlPJ++vaAhExBX08toPQs/sCbt6Tkzj4zrt0bJuWUVFMxHzOU3xRqbPVqIkOJW8sL17YGW8etcREZN15UqFpjcGTcYFMQcN+8ZAbK3FAfsdTIvRasPcG+mXF/DE+fqUs6pfKbf0jh13DrqaDIMrvhtWd6djn3cN6YXYxZCMLgWpm035IOdE6Qjsb/Gf5puD70ouXQSJ0Ixr4jls2hiZdDMra6Pv7vt+tZZPpcVn+79ZmY0kalAhFlpuKrR9LH2t1IUohzYQpE7LMvWJdsCQ9RX6TA2o6XVdGtNLDfmPt6T7tvmUgps5O0QeC1XdD3oO5PaVsYMH12ZTsTFYE6+MwGuWKYGljVq9NS5xNKcsaO1n0QfMeW2vWEMtDbqL4MzansiOtpEwchzwfvNoYK99tLdbiCfPMwR8dYlbthGwjK1CGYaHpnpzYGvdotIxY1cwedS7EnLA8+YwGyiqfsaposK6iCOyMrzirjACu6yP4SukK3OjNw/x72Hj3kK0xKBGKLLeWrsOCWKU+6y55EQKztQYK47kvfnH9M+ypVqibkZdOLvk3mpe9vXUFDChcJoNC1lvQxgeD/6PgQVntMko/t1wjGXTZi4PQz4v4pY9bSp8vEZqFAmTeenouKJatgk6qemzSfajH78WZWPymkxGwdhnDWpdt997/kx5Onpb+9Gk3SdL69MjbrGD+lriKyNKOGjN5BVWm09UFZTEc+/tLxMCaI6bxy818fr4eqc0is62US+lGYFkO1kYcj5cCC8GVLEtGM22LUul1FNRzzcbIBJ5VUGdAIu6fvH2oK1Rmm/BZ/CCVfw+JyAawWW6wKBCupfPju+/6ey7jkmB1HaZTnsFSSreHpRGBlNOMAaMPTmbh39wsvx/VuLi95Rb5wYGdmSXlSqbeRlSEyir97xFTjiLUzFtP6WaxApStrB+NjMiWA1YQvVVmnq0XMux0XKOFpET1nDz300pSgLT44S/02vBa5GkuXrR/xLzWvTNogCVE5GRZqIWXm62/B01fMhTbEJEvzIKUW1qwI0DWKhCFDQJGR2Cqh8iwiwUGsaYxrIsnC9y0gkOjYNyeNCgRhDKBcefnedcF0huxl5gLQD5XF5TyeidI2JqlkEoBPZn0V1AxNu8Q9GJ69HxYrgNWHEtapy0HaNYdrC187+Dz4g6YS0cH3TJ5CFmVKZIE3mhZv8tLu4ghQyN0wSs25uPjdSv/+nrdKPL2kjYu2dXnrGi54MbS6aFy7iIjUZ7BH9wt6m9e3NYP7hYcgm/ZcK0FhBiMzWpWaL99JvWR/VbDgBbM88Yb+UXy8nvZPFjBQ5YfChHEfRlGX5ZAnM1qffXV+PeoeMkYXDOmpZVroWhF4be0Pm+gQYkwKAqMs3gCabpAwfb3u3XV/GShkrKuDPa3F5TmxU9ZLkPs02xzt9YgvMjvDH81K9KnDzXZwyI64DW1uqklcurND6uBEaWLIz1Vf47fan6zzhCgqUyeMvLi/aScQvNJuAFku3pP8bSCgTEPlnspK8ctl57VVjzKpNGXjvnQ52I24QIVN+V5/LdObuuP9pOwVXbxPIZnGh+UCOYj6lODQv5WohfWoT2ZtKWKWhXbPAaczTpBKyu1eUI6E/fwaVxRV1bGmJkiP17p2MGd8emTdmF4CjfQrWwOvd6zmcPac6uyoLrWtGVG2cMY1mkkfIGQZPzTcn68ejzsXZgMtoJSgexYWViamBxtmS9kfngxDTc360oVa7FgyX1LEZHyS/cTQlVjKAZQLvTvUa+BjQUtynWZdsmjWTlrIRE6o0K6u7P3t2I+MJ+W6yp7/cTIqCmROajlImY1fovxUEBGa3oZ9wdjTAYHWsILC5NdFCsaV28eryELcu+t38PlIA/o8/PVymNesE/fIEh9nZ3x+bWsQmwGCfux3OnDQ64kRdUNe9KDVyK8w5T5YaNobeyZrAWs/e3R7wD7W3FV6OoLHutjaOh5aXELSIXZO8CySlYU5Gal52m3qpy3TDZei5xncxfNlyWrpWXPrGqUyp/P1w9ovWZewOPdXVv/DH2Nxx2f6UMWyhj7zcuX8bygu6eXwRFVH9bnru7QigtuCE/R3rTS6TfLZf3XZVw/Kl33z4/Gk3w6lE4/lNYGE1rZAcvyti0a6XzO4XsNSzHGzCoR0+lSCbDeBfDuyYndCChCM1gEr55bS+NtybGPxmARS0nSZXP39uw+HZmiRFuiB61EeFCsVXPE6lQo16nFGtJIRN96NdahKatvZlwX1rxoIe6hgaivYh0mx8d+AKU3P0AwEJxp1epgCB+qyUpLGa4nPZbDQ55FIMlTQPVBlmnG2KLc6HYKuiii5S5A4zdPyWDrqT/b3d38gNXXN77BzyA9397Bj+9JZfrqip99KMzYJ1aw5XqlLOrPlev6c+W6/oWvO9CTfKjVK8MTWpeX+cMNQXZejIO0eD1mkZvF2hSeVaGZTSIDXuAZDlX9udeRD79jGjwbOzvMLUtfCpvx2B+79NNq8tLgvAv8gsjzly/zPVc2oAerRERKuFe+Wh/YWpidnKwHZLOSytKFV+u6r313t/s3UzazaWg4VLPpgN68yO9m+yaw9/XGi2w4OXcsAwBuP2apMx86FA7dFwfF5Lw9qWMW8P6IefKQIaC/UQfXSMZKJCVj2Fky/+qqe17L+rGgcOuZLa4Kef3yL9vorY6r8Hg0E9gPvvJiVLAmnizHWYLMIaAoUQbOigGqlQJWqEluQG9ztvqJ8Dvtl7u8XD0AM4qJd1BJ/1w2FsFDIuQCMG0ZByk0UvZbHWRoRbUzf5cXt4EyrGydbm7WfeMMCbHQD299Dw66e7NsoJaqgj3owSoRkTvQQiLQM+PuruMVZsWwmigIYJvPu3ug1bV3MEgXmGcteW4Qz8XJjJqsm9SLDWEXelhg33iWcmZOPdnTggRZ6e9sTLLHDfuOpaTpsehMjoz8l5l9GbfX4eG67JcxdtbzZKM0L3aLzfvVVX8lgqX3wjXCXFLMgN5G9eDsmXx8vK5UyjPIqqBaytJo/971on6UmTD4sr3NaTHFdLpe5Aa/k6lbUhBl087Y2C2I1GogZV0HB7HmikBB2Y5Woym3t7W+8w7/feRuQVc4qSlGG2I+51CZVT8+E6eCroQeryBHvm820Ab0YJUI69CWCrlXvRVBY3t7q43TomBGSyHwIFqdZiYh6SiYzOIfT2nxEBpJrWiE7jXCDJz9/XXZ4ckTHDS6cR32Oasqel8XKwHOYmi0UpZRCloKIGFerNRF63mvv77udgcCkOnd8vWvL5EduIky59Hubk5R0fyo3dfbaD8gz+RoT0kDu+XZ2AdfObitPyjJvhaZYDstWGR+NNNkmYX93nv5F3n9dZ+5s+iIFWcRWQ4Sxu3jRsG8RoFumC+N1kjIC/MZBZlGh48ngL2o5NHIFpLZbKCe9GCViFpXrRlYmNoqzwo2mZngHcJehkH2UJcpw7B8UP1U9tew0EVvHDL1OoqjaInhYO5Lq/w0mwevUqZOzZQR+xcX2wumji6mRDCfulbKsu4JCYN78oQZY9HzmKIojaWWjDiJoErXj8crWK/MWukMoxbkKbogy62sKnbusQAAIABJREFURChjnkvTu2Sl21fKon5YEjfQPk+5OWUwjG4FLS0NnbfMrJ1SbK2PafxR2emMdjyddpAuNCs5dh0Ru7vbWQWTSYcuRMGm0cYCwrNYxAxuwbEshzna+FZbYfhGvUA2uaGymuuARNx/doaFDrTC4lpJtXjA2ndWNggrIsX45/R0NfDQq7AbHSRe0KCkLBrB3IhwaerYHy9l2uqNYb2PdRh4bl7EW1hBkexiNX0ig0SSdMlOJl2QoZbnuh4Fk0W6Vba1jlYFyGjs2YspSldX9veB2GaUUokoI4sl+p1njOKe0pBgBQrRcK7P3KBcgt7P6Aj6wwOlFCDVkTELUvtYlLeEUzVkDpju5ob7Yr3r8WNeLREukaywg2+QFbqSedXsEEaQmBYCLSmseizQdKNNzhjaU2IsCBIKQMSsYBZLAGfbOrMArC3Tg1ciavXRARYkaVX5k/UKdCCeLiSk9x3bb+Al9jlTZJkw9ZRQVrckWzsCxNAI2f02ciMifsnLtNKfMcXfWsOLi36BzrL3AkOs8C6QaWyfskPeS9XWNRss+SLllqcIWm7XDBLRkqZsyS75nlDWv/51/908JAKBmy2uj1Jq/Wt/bVmdWBcABD9la7tkUrinU9uYZHP/k7NF/f51YFWDMjnA+C1bZGbdZyaRHbJgGqnU6IOVKRlgBosJrQpn2Qv3ibS90Wg51+x7yDXWypzeWDo1ygtyywqjlXrqihaLOPsEqUn3iECABiWi8vWW9QdwKGJdmBIY1StgglwrrlZcFAt0YzyEom2anzx3mEY79T7IKBWZLDHLuNgW0ua5i/v4yj3DA+8l63HoebLcDVK+yd+0NPKDq4Ch1BlFIRM8G8nf2cyuv4AL7hedddR67ewss5RQJyir4IxGyz385AnPqFkseM0eJu/RdNGaGxkA67npI7DhE9KdySLtyVtky2fuRYF6lyz3iXHh/+XBikXLaP3ZKnTexZpwWdHT6HPB/vbOO+swacsaaMH4xhvr7+ZZDZZw9GI4NBr0KdCgRHxMUTEbGaE/n9f6rW91AgWCTX/fQhGsXjceb+IwlAKJCXBLyfVqmgBmZtVyUXI7w5cMedGKCasN49VjsISwhUhYykyfXH9Wd4ChxCyWxlpL7U+XhkyL3ByN4uqazM0EdM1z38n7aJfH7u763N7d1foLv8B5FvdqQYLm89gIjeIrDg5qffPN+LkS1bAqNrPfXV/H7jVvX9zd1frWW3YKP7734VO1AE+erB+88I1ntMhtlnrOtHjVkx3FK7RY6t6FOAsIPsvqwjOtNE5WcjzTYVBH0gOWbS1/aqXWWQJmb2+1qc2nRIMSIQibN8MnpSwtieNjWwixtZYWlbZeMz13LB5ivWs8JCIDn1sygM2bPGCt3jds3ChAx2rqIEYAe8MyfDTCow9ET45476szY6KMg/m8k1/6/ff3l3KtBYpvXRvILbauo9F6qiqLz7NcBpChmg88hKk1gwfKDFNsJU975+F8zqtpWvuXfT6f22nIiDnx3GuShxGYOh77Z5nk739vflc/sl6eTZg3AARRWamOmkmyC5UVlKWsB+vI8UXBnptciDi3/m5FtbMgLnx3U+20ZTNYFpTn08Ph4hUI2iINSgShDGIlr00UfH14ZnruWMGWlmEgM4tgiWbkib5YJ1ltVUdz8fixHdMh45zYe0AQR/vNcyEhrslCN9GbBHuwj2Fk3RuyPMtbaIgVKT86qybTbhxzZmWVWTKUBahbPNfqSpJrtUlMxhe/mHsue8ejo9XiiwyRzMjk1ndHYCme91q54ErE8+cNvpC6Xv0y6iz5a78WDxz++lZBmYFq9P12d1c14tFouTmzXdw8bRKCA6lBQEO8jpm6Gp72N2c7kbJ5xT2nU25lSsHmlQXGBaQq4pMNaFAi6rqPm7mz+ioK83lc8U9beFGKpefvtqzCbPqcdyEOyRtHdk9b84ng1FYFPoon03CylSmA/g6IW9vUPdu3ToVM6cxUs+yDcHh1ipiVzgwj67dZ1/bhIUflFgu7qNc2kBzvnGBy26tMqqlvzQp5Vv6xYiARaHqSKWdsbYabm1q/8x0+iJub1aAN6zsgjAXaNnxNFsTpQZpywlkgpobBsoLCakaF+2tIdm9vNd7Diw6XwkWWse3DkI8fr4/b85G2Wjj3pEg8eCVCw9VYOx1YGO0r68KejTKq9vftZkrWuJmiwfaVlRLa55KI5KYR/Nb9o+Bjaw96QYO6OB/+re/RZ552d7n1f3hY69tv84A96ca2CgpKq9+ybBFn0WctpPyzjC5LmZUKWV/XtrT6NTEUoBTeXyVz7e2touZaYdcuRhbLkEEg+irW7PrPyotPGnfVUuqHT1/wKpfWwRxF0GpU4tVXV1+EpTZJ/ygUCPSqQEqThxB4JXQ1c0UTnp1sXYMiSiXFpVPHvPnsu/BQZryUTctHGvUI0ZdM7doiPWglwgv60qWJ8X0dEe+t4WTSueRgNEwmOZdjVmFke43xcguEHl1nZ0vBytwnMg088l3rS9ZayCKVuOBqsRR2lrWixzYa8QM/ihs5OODfgQLJLPpsLwhJzIUsYyHY4eoV6ZJKgVU3gvEYCwyVqZNZ17ZnlHpGJgy0FrTKCmi+vFxVHudzHiybpT4omnf9sXJX//brF/X907s6nxtVLlsC8PSk39x0mq5EFzK/tyDPyAeoYcFNDzW9KbRi5DFyZK3oQ9ebjz5a/OFhJ1Cvr2t9913/u2ycWW1dPi9S4HrQg1Yibm/zlUI1D0pLzLKMmMIwm3XVYj3Ua2/Pts76pFy2BhV619HRslbG0dF6mvmLF6voI3z6bI7QEEsXxsLvW1LFraJ+k4ld10N/PhpxBeS99/qlrSOmC/eUlXGjNbN65lg8wOD/nR2ONDPXQda4Zd9FGXhA/roHEHgaBiHr0qkzGa+vbZ5FjN7trV2aXl8t8RxMfnsZTpLY2Toe98+ixO8xTlrl0tPGosp3kUCx3AtscQAtscMUfiiWnuTFSWRIQ8Zgeq/WQq2xxseKunj57JqZIqGhm/JkGcKqzDed9ksZ3ZAetBLhIRGsAqXF860+UByax8d+bIB+hjcG9m46O2ETIZb9Lg4Raf1bc/zy5XpNFJY+mRH0en9EB5FVQfONN9bft48CxpBG6zCSCunxcVtqLShjCFnPt+IamNGSec58vq5cQjFm7nyWSuqV2obBe329/h2rRTkLiGwxHtl5pF31llKySd0kXNJdtlblslUY1OoLFMtiwr+twxcMxqBQb5Lk5tUZJS1+/BZtuNY4+jXasBFUaC08mL8vY0g4WFZLQ0U1+OfQ6VE3JtsyPWglolYeE4GN7xUe0/zTp6jRfN4dpOxvunRxy97QBF47Pc2ndMp9xNxx1sUs/OiSMSjsPa0CX/JilqaVXgjZxAT+tvpsQBGIxqjTABmPZArPZfivNe2cye+M9W5lh7BGhNGYIQflvCIY3nrOe+/ZHUxb38Xac1puTCbcjcMaykV7wZoH+e+VKpdZyz0qlw1LPrJWIobx0I8+cQVZRSJTRQ2kc8VnsyWzRcU/MAdeERsrVQ7tX60W5hnhKQuVsGI1MuZjW24jhx68ElFrt7c8AZ7lS21RRfyAtGP9bG01tewNTbreQgZVkOMej9vKDPd1m8Bn7R28Xl0LhkSwMaPioJybvhkUXsVglo6qYyGyiiero8HWWMpDr0oxo0w1UZxBMk7NKrTG3uPsrF8g7vHx0tDKpN2y51hBnKxolOUCk2cdGwMrgmW5rWezWr/2tdXPnjyxZdHe3rqL8va21n9+noQotXDSD/G6ALLDSG4eWchFWsfWIevFFVgIR+YQzFpblk/u5iaXY59RtKwqmF7l0dmsG0MkpJkSqOcr63/bAg1KRLVjI+B7jfgSsKYWFoDiowIzfZohZcrrtlpae3scYYPQ8u4FhK41IFLO9Vtv2XOE97EOEN2cyoKq9fcWC17yeBuXDDKdz9cbLvZBhbRssHiD8RzQNWsPeAqc5tGnT9czl/Cep6frfISU1RZ+lO8DHoiKV3llqY+OuvV4443VeWSosBUQi+9a8oK1ikDwJlxcKHNgyRXrHWHEIs7oCwckPoJFkFoHmn64ZTHJ1EUEL0HovfWWbRFHWi+LK7ACCAHNyuCZlntrZrd6DFhRwV7kNjsQvMwW6/nHx8t38CL+Ly7ijRTFg2yRBiWi+rzLhCSrrMiEyuFhB+F6qXlZ5dkqs8t6v4BaIsU95ReHyfm5HSAm3XSeSwCWHuN5y5+Md4oOEK1wWPssi1psesmmbO+/vx1XiazzY1VX9TK/NMolD1CLDz2jSt8HyibuJePpwMetNVcQ5OytE4qEyecAgbPuq5V1edjPZn4TLSbjI6Nd1pqIUH1LHkm33pfKbf0dnamBCZvPlxG0Fxd8Asbj1aJVljDSGuHubjy5bKNpocssHyt4az5fh270Akb3zmx4q6b6bLZUYDxt22M8ySAWEgEmu77m/jr0U8hsHG/+t0iDElHXrSwIvyiQOXP4HB9zIX91ZR8ClqsiA3/rg3QbWRmA4b13hRJd6zJ4jn0fqIYu+sb6aujnRzC2njcr4NWLTdhG6X55nZ5y/trk0s3hWFVF7/cw6liqpj40F4suA5Dd5+234/2g0RNvz4xGdpoq9p9lwFlIXIQySTSP1YvxKkrrmIhs+AD42auGyRRmZEbh3zRTg02eFVCEBlNSkdAWU19o0dpoGWqpjHd1xQ/KSJHwhMMbb6x/DkjZUw4sAc0CGzHP1r28+JDsmvSd/0Z68EqEZWW9/34cm5Kx9JHWp4UFMnvYIWApkJlocs03TLFHZghkhUwDZN/NFDOCoNfB1c+e2dZc1OFTvpOVORbNW8bFCcI6W8Gu8kLRI5mSGQV/3tcFpQJrGCmOmHPrcMsWWNOyMRO7Y/ERDuHLy3UF08ui00pzq6J/cdF97/ranysrvZsVUoz2rBULJYM/LYVMI57I1PjRflAS92d/dvWzr3zFPqTkC1sTk7mseIRMoN/1dS4ileVNa0jJSiFltf+zFoveAF6K3vPnfB7OztbRBo1q6MY9Vk4zy6OXZW/vkR68EmEhfZOJH/iaLd0uqyVaJbRxCHhuvFpzyAfbt6en3Xtooe9B2aV0h2nGPSAFIxPyVmv76Pl6X+vvoD6BVx789na946mFguI3Gflxc7MuD1uaGmYurFnmuy9f5lAnHFTRgd/i4sH6ZOOHIiRXK5jyt3DP6zX3Yt08FzNkrLWX4fKHh8BzH1r8xOaEBRHrHlXaDWLFJV2cdhP20cxYMFbDHAiE/i4rsNTXD6ezKlry1Ft9jNKCZ1XktG/Jsv5YhgkLMtJNVryx6sqFGZdH6xycnHBfoQ4Cuwd68EpEJuaI7bM+vO25L+A7jxR3jTZafltQNu0a38O7WQq+ZZlCMDKeZ30HpDyJKmoiponFpliGTXafasrWQWDukG27QuDyyqC7LKVU8irQr6xVz+D0w8POgGXzMZ0u01QlQsPkV4Tkevwpy5ZLWavnXrtRWGaPLGbI1m40iuM3IiRE8yL2oIW8yWJg4Kn9/W5OpbdB99+6vKz1V8aX9V+V+XrPDasoCmMqWSBEB7rAsv/qV2Pm1YVGPG3KmkC94b3mYdCALeTk5ctYy2djRiSrt/CR0Mhq59nocPY7HDJWPMc9xkY8eCWi1nWf9SYBcDqNkmUDZDsDWn12LHiVKSCRZSgpA/3DSvzGN1a/9+JFrJAhcLwlSl/zf+bdM6iJ5Srsg/ZEWVl9aspoaDtSUKyGWZhvxh9eqWsrGDijQOsEAbZGDK1uiQWKFJ5S/GaTkq8sWf366/G7wiDFOWsZ2Xove+nBGB/jqdNTvgfwfq+URf31clI/LLP6o6OgcZR3OGqt7fx8CQNlorW1b8ya5AjikS8Ll4EXBe+5X6L2tpb7JXL7ZKDUjMKRhe30hYA0K21of/9eYyMGJeJj8uqwtFxM0GprxfOFgjJ5+xG11pdg39/fX4dYrch0qzOmlhkMeYA1q+fGcz1Y6GikwEfz2IL2eEGTsr7D3V0XiJgtPCTfOxN7I8+KqOMkZC2raQCXAXvGG2/Y8QwWj1lrlI1VYSW0wUdWbIe+ZxS8bCkZGX7GWDwea0Xmo0ujiYzf/8jhov7mhWPVwy+LfFHp67SsD0+TBcwDCFMrBS3FZkrJR+TO50uYBt9r1dq9io5sctGmVr6fFBIeHLdY2LndXsQ3irLod4sCaSym2SINSgShvpH6yDJgPAf3WeZgtyxBVspdk1TcIyTCs2jk5VXvlGN78822+dLjYha9hdJ472aNE1Yg5OfNjZ1yLo0Mq3aOl2nF0vWtdbXmA7/1gk7n86WciuLJJG8zo8yKa5EynR22ljJirZFOA7V6ikSl2jPNvrK1XixXGSurbbnJrD2dRaWzV0tfKMrUWAD4V9B907OWDw58DRiph16+sNRysy+atQxkekymxj82ycuXXYCjVXTH8pVluuox+M+Day3YVwaVsXxhvcFbK81tSIMSYVAmnRIBkaiolz3AItegZXlGhduk1QcBa7VztixEK8MAh6K3jyO0UM/ddLo6Lsvy031EMEeeMmYZXpgPbT0zxCMK1rNcGF4sU7aHCd7F4sPj41UliPGdNuYinras9lL8uBT2mcXHrC29VUQr6zrxDFwYanqMKPgUucaYYrZYxKmj20AiLINaGiW4vxVwukZ94fnIqpIM++ab67+XRTAYDBZNZKufEdHkTGGZzbqIWe13Zi4VnS5UCvd3Z9MpvZodnoCRSpLnv7697QSpl/WxZRqUCEFybTLWg1VdNApAlAc7K/Lm7XNv7BbaJ0upW9/F96LOiduEZWG4QMhbsShXV+vv2xK/gbiASHZF6GlWnrGuypIwz4eHy3RbZs1b63F01P1G+tgtixzGnJeBhgv+9siqteJQ9GdMIWUxfky+ZVw4+C0OUPb3d95ZNQ7xXdnZ1D10nfdlPGDdryVGEJeXNox1f/p0nQ9cg/P2lk8W6mp7RUM8wTabradBeUzEfIZRURdphbNnwPcf5ZlnXSuRhuq9n0UWEiGFBkM/omdoC1K7TAYk4v6VCBZHFPEPqpgysqyVSCHHWrMobEsBrdVXeqSyA9+8lgP7+/4hgywp7aL7xV9sQyDke2bTCa2OphoO18qS/l50iKJmgDWfMgDckmOyHLRHunovQ06sOWEIiCfvIiNS8ok+K/o0UrQC2ktZ9t2I5JvnWmO/XSy63hPybyiFIFF7b45aZSxDlSxURbvGWoxqqXRm9pX7Htl0NA3P65fRwSpRC2qWf63zeJllwGIjvNx6i8F0kGfGpRK5cEpZCs5IQMvxa0Z9+nT1O16AJGsA4wlQBKDdY5rnoETU2HfrHT5eLY/Iqsvk6ktL3YLWrWdpXspYP9YlYxNg0U2neQWCNaPy5kH+LrIA5QHRN46rlHVjwOMJNs533rHXKLOWGSRsOrXl9ePHdhBi1g2NdbEygzyKUvCRQWe5P/RcMdd9BNtHAdIW2iVLa2eUQPBthKqwtY5QFtb2IONCKSURN2UhEa03yvpoJhPbCvByv61OmhlBF0H5LWP35go5wAcHS0jZy6WXzDAedwE2bA4sJALror8fweanpw5DbE6DElH9wxwKs9XvIRI8nsDMBkRlI9nvo1aBPABkbZVM/wNkYhwf27EZ1jxYwtQKlmYGTEtTLd3jga2dpUDMZnasC1Ma9NyxNG5LWbq68t+LKXVZJAJ8ny0alQnK1ePXgao6Fk0HvetYFlYnwtrTrU3Vnj71FXX93tH+tf7OSl7j2tuzDZPMHFuByOFN2IaWGQ9awLVEi8rAzcUiznH3BF6fKFVLWOrSqHDh6Jau4/Gq7/nRo1wGiFQkosVj7h5PyGpG8zZ4FEy3IQ1KRM0d5lbKpbaWmALaV8nA37P9H/AsoAQt+yxzATLP5M+/fLn09bM292we5J7e27Pnkh2uLIAv6pLJWqN7h6UVtI5CYVYRsYzRg8DFiDeyRhTmAL9jChFrDjefd597NRws6zqS7fqQ1l1NrQ6yXnMwi9hZ1Xoxua7f29u/1pycnNiI/N6ejWDJMVgIoOxhYxLzV1kCDvXxGWzWAvWhhaolPCRaYW2mq6suk6K12l+U6xy5VLApZHBVZgzy8I42CBPoGN/ZWQx5ed0JPb/7FmhQIj6mjB8YEC/y/y3LtDUl11IyIleXZ7FY3UM/rYsJcE/w39zY/m5rrTyEgFn8bIzZgkfWemCMloEVZbRE78p4I5PhoSP4rXux+LaoQ6WeAzQ4ZLwKNMqLR/Cuo6MuhoehCkzxku/V2i1UX5IXPOO4df8iszDiBc/tFfXeCGmxqN+/vq3fu150v8lCN5JRt9lZTioRbOK0RbC7u0QExmOuVekiN2QOPlk4+MGurtY37Hy+LMkKGCwzV9Il1IpERIykvx/FutxjD40Hr0RIPor8wCg/jLbDFi9tCz3ylFftKsS7wGfMShDrHjzPnvWrprgNoSzJkkXRgS5jDOR7TCZx/QAp0LN7uVbb8mQuHnSBjOQh3lWXPmeGEvgi0/gty4OYS0sRkDUnLJ58/fVVlxWyTmQDq761Eqx4DusdLXndikzIw5wpJBn+1JVds/vEcilJ98/p6TLN3DO42di02+g3zpPIgvTzWszSqr0x7UdHcLPfvXy5TLXZ2+PCLKrz/7nPrZcPjYRiNmtDF4uR7yRdIxJm7AtZ397aYxqQiPtTInRWjNVNc7Ho0oqZkGEHQqYoVIYysQcYo5UOCD6WdV7G42WsTbZuwTYu7ca7vfULNrHAbF3L5e6OFwTKVB6FUaFRDS8F27I8PehaH0LjMS+qJV0/L17Y7p0MkuxZ6RZ5wZxSWbJk+mi0rI6sLehW9DtzWYe49R7f/GbuvjLWzRt3hJS1xmTI+zIEC40aP/e5dbmjA/wtsuKm5vNa//l5kEIpX5rB5/DtZScACoDnbri97eB89vuodri1SBlmRPQuK697cLB08+iGKLBCscl14KQlSBjsJIUcCyCSFkYfRt0SPVglIstHXg76wQFXWqN+Dy1jjKynR4/8jKdMoJxGYDaFgdl84MDW+8V7FkqIy8ZDsrPq0ZFtNEyn66nuWubIvjUseA/73tvfnisV72B1IJVjy865bjJo1SLJ8Jp+h6wc8tyvCFBlv80orDhXnj/Plfpm+8zq5BzFyOD5uvCbdaZaHZ77KksSAe1zn6urOE4kNFZxOFmaBgZnNXqScQNXV7wICptoj/p0ScRlFSGJYLGzMx+esywOy9fkRbyyhYFVgc8l3MSCQmWAjpXZck/0YJWILLzqIVs4yPTnx8e2gilbiUeKRWaM87mvaFhWjd5bsm7BttGJ0WjVpdhHSenzGwn/soh4nbZqwceWAqADBK1CdhcXdtAl4qay2RPSVQaD0CpsB/JiIXS2QxTICxnp8Zz+GwxUT/mQ72dV4NSXRKr1+/RxIzB5642DuT29GiLec9l51JptxQpdScXq4sK/30omoHYnyHQYSzChYJXcsDjUnjzx4fiItM/z8eP85PbR9CQE6sE3TIBbTcCs+IwWX99kYlsrGqLtY7n2oAerRGwDXmXBYuPxEpa23IPggUhRzIzx+Ni22GSZXi8Iix0o2sLNBmkiZqRlHrWilkEpMxcOr1rjmhxWzj9TAFouSxHBwWGhCdYVxWppFMxCUSx39uWlHUQokZrWWBrWXI1dOgvE+s3hYWfoWjUhWuMfJK9o0oYfW2MoYFF6v0TH9Nks971U2PooJdKAwdxEc7IWy6Urom0iPKVG3/dgu7npomxvbrp7ZJjQSlfB5LDfMN9QS9tZCxq2GGwbhxEKnXwG9GCViFrX0Z+WC/ncOt6lr8VsIXseKuCVooYyg0PDssIZ/7J3GI9r/frX1z9Hah6EVZ8iT/N5JxeeP99+RkmkSEGuWV2RW9qW67VhLpFs5d3RyE559AxCXayMBY567i99AHnjHY24i2A+z6+jV53Xk636d/rfR0e17uy08aB1mN/ddXNmGYFeKi9DGTLxc5sUTWtJLZYXioGZA2G5plbcALv6BOpYE/PiRU7YooiLFeikoTydYyu/a/np9PfYxo1SZzTyk/G9yWsyudcMDI8etBJRa67RlnUh4AxCgeXXZy8cOtoyiSLxZbyA1ZLYiom4vW2vGaPnCo20YGmen7dnfuGdPTm0SZwGlAGtSMHNYiEngMtb3TuWUigPj2jeMWbdI6OlWBlzHxwd+RapVTHVGu/Ll+vybjzO7QVZpKulzkIGZZhOa/3VX42/x4qM1bpuxWfW26ohkiVrPWUtGhaUmx1P5j0WC2MgYB45WVLLykxUS8pQNDGtl5VyZ2naTOOLMiRqtV0ZmQIeUGok42Uhv0wTmHuiB69EZA5R1vlV85uHjrVeMmA52j94vi5lj+vwsNb33uO/zfqe5TzoND6mMLcc+Ht7/iEFq/bb387dD2mt8rO+bgnpCmmJtM9EykfzrovdWZarVtjQjdRSjq3GhpqfsuNlbgoYRQzhYjLYej+rlcJ3vhOvAeRw5BoDGtWyNriiLA5rLvFu2lPgFSyDMsnWDjx/eBi7rNj+k78zB8JeTC6cZkQGA7V2ksT9+2hEWQZnqZGIMmU5//KdGeO2xkNEjDed1vr++23KBIJbh5iIT0eJ8Dab7F3iBZxtu7ul5nX4WpnbJfN8xn+ypH02O+PgYCn4gLxs+p4yQ4LB5ZbgZO81nXL/eF+3BOan1RDK1gmxeCqbInx3tz4Hk4nfjdUKOMz06bGy+ixXsVVxMyPbNBIAQ8sqhmVdk4mPXDBXcrYOh0abMoZqrbbiZwXpW2u5v79EJljF3MiwkdVWV9Yjw/AIlLSipZnl5WlVFgN4wWVakGQgZRZRzr73zjvrn2mhLN9fasRRWW+LPC2yJQgJ3/2U0IkHr0TUam82XafACji7vo6FDhNmHl+wMsNWX4S+ivpstgz0kkIzxogIAAAgAElEQVTIC2iTSrmldLdc8sDUwtWbn6Oj9RoP2CtW0TDtxo1kEjsgMnKqpU5Iti8K41lrLNahaSmi+E3Uwpwhv+yeFhqcJcsge++9fvEBZ2e2y4qlY3sxI/hNpp4II+vMsrq5emcnW3/NO4tFF2tkrbm5Tl4OceaStRTkBvWCNaWF7y30ZLIUXDJKPevrySAR7D6ogBnBTtK/3KI9W/e9utqsKVKL8taDBiXiY8oG37IU3WfP/DVE4yTt/42653r7CQfk+bmd1r0Jv0GYWvA3rHu210aj/Hii98z8jsV7Wb1MpBuXHbaoRmrFVmXmunXPZizYFhlrKcRRFU/Mlyfr9FifPVvlY5ZimqFM/EWGp1gvFAuFGo1WxxpZ7phDq55Ihi4u+L1lG/pNUHxWnNCK6dHlBXQGz/euu9LYoVblDUYylAXB6E17fOy/OO5r+euYxsi6ZWKymcZqwZ/zOd9IrFOoV0jKIr3BWqE3dq1EzG6fBiXiY2oJvm1ZU0TZHxys7ikPvYjKDKMvghRmKMDU13DAdXS02nNhseAtiCVkrasxAqXQ+/DoqNbXXuMoQTbA05IFLWsI0gZDdIDq32GfP33ql0vPGiHZiP1sSW8pE1viX6L23xgry2jpEzun3++dd9pSNNGfQwYZa4VMGtY4p7TFHs3N2Vk7j2mykIj33uuQIGmk940n1FVePXnFKjgjxgJ88BvnjUKPTY714lZpWQ9RYG17vb9Fha00dBmlxMzn+Xr5fRimNWA1IwAGJOL+lYhaeVpbtrxx9gJMbgW+Qbh5fGRZV3BteD7xzMWCsK19gHgN+Gfl+K3f6ANzseiQGuvgwLtAuFnl8KOUR0kYgxbcWWLvwJQAz3WaUVjYPGZL9+PSfvIWlMiKz1osOJLWavREB6Xl0vIUP2tu5Z7SPUky+xpzkeUxizLZS0+fLmP75vP8es/nq9k1r73mf5/FtLB7flISW1rIGU0PFs+77/K/v/kmt6aQo241J7IsMKkEeMU4MEHwiUoURKIHbOIfPbJ9qZpaGSYDyVmXFUXc2hGykQYlQhHWzoIs+1oH8vrLf3mVPxGDJFMKpWKsyzefnnY1VzTqIJs4WRkZ7ILVwfajdhNk2lJjH+sUbKAUkrz4C4xNfzYabab0Y36zRb8sHumjAGBuZrMlOuUhF5YMevIkt7YsPiNbwAhlxxkKa8XDZGPIQNnsKD2uqGKyp9SxCp+RxY5DvW9bcq1wZpR8qShZZ7C1Z6N9JfdkJM9WSmJLiD6rjXp5xd/5Dv/b0dFSmGk/sIUUaEHNmrhIRrDGL6uunZ3ZJaylVmoJBEsIsN9sUiRkNOoOBql1y4Y790iDEkEoGzfTqpR7QhKWMPNfzudLi9lLddzb+//Ye7sQS9fsPOw9vXfVrl3d1ZOQIVcZERuCwcGEyDITIxsZj3UkjM8BSe6M5xDP2N3CfUx6+kYXpyTDaXDl3KRBmLIDBe2LCjEd6kIkMLlIXdiEUMGmEE5McIGNbAIJudgytkSYSLGs8+Vi9zN77bWfZ631fntXj0TVCx8zp2vvb3/f+7N+n/Ws9SZOVebHX/qlpUOQYUK8MMwUQNbXoTc1ZC9Vdq3SrhgR50MlLB2lN/38qJQO41XweyuSIxFAsvJOYw1he69tyuHtc1Qqm77xDd4qoHeN1H6bzzdxTQ8eLDkwTk9XzLSe5rxSquqLDE5O+lko4ZSz8+7lwYsXfesLbhek9dTn1iJ1u/Ck7IFg1o7fuH5yPTmTjzZkodDs+WFdMSHGDiwMJZ8n889qN1BGIzufr4NTbVtmML0htWIR8uo5bmncGxFkRJU2qkR4m3JH25eAeSjwmnvxDmCTxH8rFkR1+eoUP8bIEk81PZaci6X5MuMv8wA9HqTyvtbzwxne2xuGP/knuWGpfh/Nk9j9mYKrGK1RdMXLNQsYVCSEnojKP4OvaKniPCzPgVrragVLtEZqv6k9rHAkzJFU4ER27zHdstk9ENHy/356WndqfE8UJh9mM1cKuk1O98EDbhGhRDMD5PjFVnmrCMjVS/zCroghj1m5WX5aoWgPD9eNApaCYf0XKh7Rjsa9EUEG2xu+6RLbI2MFgxVyu6R9tk2eEP6NykWt0MBzZee5J6pp3xVCa2wkguXes/RjRXZEMiwyLivGFBwL9rf9fQ6YzBgm1VVhS2TR2EzWMS+bgV2ziA2Lrrx8yd8FmBu1rnYwLgurKJX+Yr97fp7vKRVNgV5Q+6JSjZitrWpoNuY84l0UY7ONcG4FtGyN92T3XhrbqBWlaK159bK76DCInFqEjmfPu40QOTvjh4eV0PUCdbYY90aEGD5a5gU5M/RYHhLRJgZC8wpLAZjHNqSKvDXVObL6rv5+EaMeBB/e1XuhPT0Oome6uuLzb4Vk1BAt+l6kWCsVcPv7qzJf9Rn0IPHPljU0m83yNYswAlHaOAvbs/tmESFVcdTTLkClabJmiwwTwapMWluuV2RMWSPKf/fx4zg6aQ18dMwGsdRkstwLkezZFXDfOs0qwMD6m/w/x4WWrNFG9/+mgC495ZEKrd7bY71i4WEBlYW/v68R3WpDPX2aP9fFRS0KdB+J+OEbEcOwEpCVVtr2OxAO1sPLKj8QgdsmEvHBB1zo+/dhYVC7T71xnZEnWeOfNWWazVZpgp5eJcorYu/GiKqYB8wIv77zHS4jUMJqI4fPnm2uY9Upm0xy2eT5ebL7wyuNuCZUxCBT9nbPRGF7Pyre+1gFeHjY97utbfZ9smcU78X2D9b86dPNuc3wPFkkgsl4D6g+OVmel5OT5W/BqDg+XjoB20bk/bMoJ5dlBf7h5RaLyKyuyaSGYsfEMmODCRZUh+AFWZqDCRnGWOmf4+ws9oAUe5tCqVdCjvv7sbW9wWF+++PeiCiMirCt3ifyBrcVCjhf2/wG6z3R2vJMqXeqki+dndWbJ71+ze/LmtVdXekzbOecKRmkHP13Dw60t/f69fgqrOyCfLRrGEUvLG5FRQUUC++Y6rPKOahgU6AYe/c8QKVVnhCso4qc2P8GGJ/tO7vmw6BTCfP5KrqhjCVl4Gcp1CdPtsdSsMuz46KEGO8h15J5RpeXy7wUrCHvCcAiqwgMdbgq1rC/V6+QnUyWHgPAaBbUWPUe0KFRHSaPUs9CjpXr+fP3FoHAuDciiqMS2o1GhAHaFdtka7yip9fzU4YuayylhCkuCPxqGtJ61kxgeiX39q02TD79dN0D76mYOjnRQDwL6tzGq/aXKo+MsBwqMoMR9QOqOno2IsfelXV4zkifoBg//ZS/23QaK0wVMfHVgBYIDz3gqyysA6xwSWPW/MWLlVIGIZaiLNjGGFW6ZzJZ7f1Xr/R8RukeMPJCl27stUiwWevMkrHYzcEQvBAC2URnxoZts8zuc3QUt92OLNBM8KmNquZoV4pgbKfULcadNyJ6MDtjQrvZ59hePDjoq6Lwexb7Hv+7yyZ4ng0vOuOWar6awsjyvd6jjX5fNafK5tZGTtjffXrHh8J/6qd0p8kPPljOBSq29vZiFs7Ke0ayI2sqaOX53t5SntoUsi9RZPdShHjM62dGi78voisZ5sB6z/Z8IVXYixuYz3VU6/BwHaBbPU/w5Hexxura2xuGP/Wn1v/tk0825z9L+UXPACLIndEO4OHUIuHBImYuCyxRm0gt2KNHS68dZCjs/qw7G569qvBVaM/nSc/OllcPMKjn925x3Gkjogez48cuQrvq0B4c9JFFMaGC+87ny2tXYVDL8Z8JUygX5UnbcKn1WDPHovL7P/qj/N8vLmKZYVOUYw0Z/F31VEFZO2NOjPZqZoixiMBisbn2rBSTVUaw0kp2KQyZHyp9AlCh7VsC3MLFBe8/FJ2hzEGN5O/5udYPUKA9Cj8C+vpRdW7VngRdOIsYsGf2JdyVkusxadx0qBKv+Ty2+G2+x3/uyZPVgzIgVoX2NaqwqKZFqkqhteU7sLBSZOi8lwWKx501IrbFOSjjtqfsMAKC7aJDpr3299fBWWMN3p5IRCZ07d8zj5VxVjAF+cEHw/B3/o5OcShAGmrhbYqyasiwPDzWV3EfZCXD9h0xNxkXiVWsPmIWMWTuouKtQhuu8v4+fO7J2/Bv8/mmR6zOIaLnvZEI1ZjNy4dqaXNUecf2Pbsnou7R77CWETY1VS1VzX4n41IJFz8K+TIGLpWngbWZAaxszgovhvRJ1oAGZSvsuasHRoF3Li/78A/YmBZhi5Cb/7f3CKjEuLNGRC+ozI9MMUafq3hRi8XmGamg+9Xly7CrtLj2YpgIRHOYcvAMtAcH9bBotbyQyRGUyvl/n0y0YrHPA4FaMWSi1s49HiszYH1VRdYt1lL6+9C+7RHi57CnIkiRC/pzw2Sv3QcwZqt78OBgGbXyfESR4p3Ph+HDD/n+sO+C/Yv7KefXv2fGPPnRR5v32ttb6QNmRKoqroxGQLWTiPBA2HO+5DpL9/XwQa29VGQxK8+BPcDp6XY5WoV6PThYWuqeVMcziFXQ4R9/zA2mHmIdlgNTB6uak7+FcWeNiJ5IhFojRVGtlEFUfseUJQQuPEgbAgcvQ9Wg9QqQvT+LTqBufT5fAcM8W5/yYqzwsh0oWXSPnQsf6vdnureb5cuX67KBdXRkTIqRkR9FIuz9smfzOIuqrPK/q9JjWEsPLjw5qUdmUTWTsUcy2cvWrof++fCQ/2614qd6NrKUQnaGDg6WTa9U5QkwMZHcUOeB6Z4qaNh+Jut/g3SqpfzOeutIPZYJWnzx7GyTwEMtriJd6llwKwjYAVfPXaUmrlLqRgumEM7ppL/fcWeNiGGI95D/DDOiWWos6xpZMVI8mO3Jk3XGOChiGBr27H3wwTomAn/b31/vgKnCwD2pNzsf7H7ADPnvMf4M+26s+ZkSdupMwujxgtc2XIKRlvWpsGe5knqBnLPre3KSe3j2O5V0lm3/Psaowjwx5eSf1bLr4n39HlDzwdYJ+6AqUxlfAdtfY65qMUBrm7gTnyrqqQCqyA0Mhi+0jfuyyKJl7fSVhX7P+MZrZ2ecXsFzlNBAQxTyjcouoYQjT80K8B4kugVMKotN0WafntZ+w3oF+A0VPUFIbm9PKyM/yay06Ic07rQRMQy5cs+M6Go0o+d5KkJIcefj/J2cLEPYLLqgDPkxnh3eV0Uj/Tn0AqoSzoZRzmQRwsLsO1dX/F2UAmNyKKoCwLmtRKQq62o94s8+q82/TQ+Ncc6OjpYg9fl8KVv39pbGAgurs/X16RGFJfFzO5+v9EhlDyDylu2vsRciUpkRpqIuiAiMMeTYfe1QKTP73WwOoyhrtmcigy9iuF0slqRUX461IFFnHXlq2HTqfsq4ULXwti+F/w4YIysGizd0wF/PFgphtuNjjrKuLtIPKcVx542IaFRwE5VoRnUoA1hdETgyiryBj0ARp/UY9UzJZh17ey9FLQ/wtM+1Z+Hyhw+X89zDHhsZjJWIVLVSAAYBm7cPPljhSioyqzq/4AQCW6ndC5FxoDAYVZwDDKYIzIjL33M65fOEKJzlifBR8hcvdFo62/sZ82YF78fWLpIb5+fx91VKE6XE2f2rtA3VdL7fF39x7+3wr/fmw+8eFUqw/MQo3vGolXalUyGzBisvB2PA9iLY21sCxhhghx3kqI8BW6zKXFW8nVsa90aEGzYXX2lChO9sa/SNEf7ZnlKRN1vz7nlgeqtCmAHMGn4pAdXzG95rRWrC/rZPUTCl0BNKPz7WkUgbIs72SU+UQHnYaNscNSi087BNWW/l+VmaospxYnEjdv/3GLA3NyuqaFvWyFJOHl+jAPJVDpFh0LIdxj3SPQxHgjlQ5FN4boBis/3C/v3igvMk2Xv7/44iDm/f1nAs7Jx/tS2GH9+/Xjbvwg9mGxRlNhGDmFeSNzfD8Pnn+UP69qW9RE/w0iwQk+WKxgj0McKj4u3c0rg3It4NJnhtadltVdBgD+/CY/f75uaGn1MQsTGEuDIiIBg9ot0LQcahYgUU8yjV+fX17mPSS74dujU8/LOyZ8P8ZI3J3r7dLEtkpZRoUoaeDKpfkFIMkXOW4TR6Lpaj95EmFrp/+LAG9lXGeBW31tqKkdTutZ5zx+b48JA/vwLKR/M8nXKSxsx4sJ/H2fz61zfPo434MS4QOOseY5Sl01WKSe093y/HYrLkui8WtZANPPuIQQwPFqUi2INgYqroXr8h0OhGTaQSwL2Hj4Vae2qeb5mA6t6IGOJIlmc+jUZvRCJi5PPXbFbz0uAFWEXJDCPF7fLLv8zvi46GOMcnJyuFaAmCmPCAIcHy/Ht7HLuxt7eZHszOh/q7b4duh216ZKsxmNHgQ+VeoShCJLvWvlxdVTvguZR8idJozFucz/tAiDZibP/XzmMv2NVejBgLIyIp9HtdzXdlKCwLIz+8uOD3zqpvbDt2FhFhQ52j2WyJX/E4FDyHBXhCx1T06cHBMmppe7Aw/Q4eHLv3elua/+C89nrpAOCwQz6fa4MERoj3BneVa60e+N77KAvQWp++Y5sSwveRiNsHVkZ7yTOfKkMhSkOx7/SGt1kpnuL4Z6RMUYqmImQsx8TNjVb6TC5MJnG0geETmPE8JhLh/15RgvgMqzZRDc4iAydaayvPvEHAiPb8+6i0cGVdLQGZL2eFzMW9IKPxb4zXAB423icyzDMlmsneyWQzYlBxuPycMTnsuU/8O/v7nZ7WUgr+t3wnX4woZRDpgywlUblevND63fcPybqUhqWsKhQUXRFgKBIu7MBUQUo9V3bgEc6CFweL78mTdQEQWYCVtMUugXqFceeNiMwgtgJPGQpsPT3/v/9OD9AOuV/2t4gRj42e2nxcUDZA7ytcUEQpnb1f1XjOzof3yFREZn+fG2aZHLCcEnZEZzpaa1V6h/9WBgYbPYapdVx83ryihLwx41NjEQ4gk2mVs8E6MKsUiY2eWbyMPb9emWcGnN2LkfzAnChv3RM3Zfi+iqE05ozb6+pKRxSr62QzDD5i+YMxhioV1lclFWI9erYx2EtuQzoCZaHq3WHQYOOgKuP167qXF9EdW0bBavh8B+POGxGRQfzgQUzdnCkJ1lY7MiSVcFGfDdv0ktFDlmYvJrDZBXKanntjfnuMZ6b4vKHn+2Cw91Z5X+ulsmdW+feIOCzy2JTh4Fkn2fva77HoCWSV/zcfZs+4A5QsU+/HwKFA+WdjLKbDrwnWI8KXqLOi5gBpmF3gTvyzXF3lRrh/ZpXWiO6xtxf3RTk/59im6jqxSBVtQLZY9GMGsHkrguzDD3V4eBhqRkwPTfB0mqcU1KQhD5jVCEf3gcLpphTdbuzciGit/XRr7Z+01n6ttXYsPvOfttZuWmv/uLX2NrvnbWMilOIDAA5CXIWrmdeiLl+Jw76HEsSoCyc+A48Pz/r6dZ/hfXDAa/DHXNi7AAwC88OwHPv7m159hCmJQvcRWRRkTtUz6yF8UoI1Snfh+SAzGMhTyQ0W1bL/psCfTN56482mXCt4MNvESzle22AWetIyrW32rako+cirj87LbUTDZzPuBKP0linhyv5nF2jhlR622IjMmY0Ao2l6/vpaH8zZbNlRjP3t4mJcqMVvQBaGBpENHhyTBQ4HGxpkh2QyiVMK19exAaRARcwwyMi2eg7cFmOnRkRrbdJa+2ettT/YWttvrf2j1tofdp/5D1pr/2tr7d9+99//bnbf2zQiPP5FRbOU14891RNG9mFTxvfw7Nm6gGD7FUIaf8M+wjmwSo4JvcPDZfQA+dpdCUQbyvSKkzFwZgYzS1FUvV/gGKol4FapZEYEY7ZVw+NSfOoii2Cy/DNYSO2/MfCnAhCqyGkVxAsjUCkLRbNcjbLe3CyBhNXIdaYfemUso8Cu4Fxu44LSj/AyKvqDIgKsQ2Qgvnixvme3AZRfX/N98YMzFqUUcEj83wFaGjP5rOqBPaBCemOzo72smsiLCz0xGXOYJdnwDVSUd6WY6VhHyFsYuzYi/nhr7dL89y+21n7Rfea/bK39fPVHh+H2jAgVEWJGrsX09AJ8I9KXm5uawAYuocKjYq+skybKKJ886T+TrS1THf6ZlNKbzXi+NRLmLOIJEGeVtrtCCwz5ZBX8YhErsMPDWng+437JvFpEUyqer2+0tlgsI1YMO1Ml3IouHxGJGqb5qEnUR8U324LhqdbNz2mUpoy+Y2U1I8Gye9W/sy8AePpU//7YLrqQO9XSYBv9jqKan3++DsjeBV9R1Jxu7YdUbXQUyvDfq06e33C+FOjFC11nbEs6I0v79FRPyvV1vDH9glUsOHW/Hi9ni7FrI+LPt9b+tvnvv9ha+1vuM//9O0Pif2mt/YPW2k9n970tI4IJ70ePuLKBl2rXlhnK/rL12izEXU0jHB0t96ZqZa0uu4+yHLEStr41s9/zTHApciamuCKDWUUDLi64fGERUHsuI9baH/3RzfAwwHjKAMmAgmlIV3wG12TSR2nNlJxKkWyD4u+Vez35c1V+zLohe0PEPoNKUzJwrFeabM97cjP/e/jvi4vlOR0DNM4ugJvVOmRA3LH7cUxkXAUSLJbm+noYfv3GhOnUwqi66igi4C9fVxzhCtRhrPyOL4/LftNePWQnmGTlWb5+3XevkWPXRsQTYkT8TfeZ/6G19t+11vZaa3+gtfZ/tdb+LXKvv9Ja+9XW2q/+yI/8yK28vDosTPiwQ5QxyUV7Ykw4FOH8HgMc2AnrXVXP3PPn699TaHvvcT19qiMISomreVJGhG38Yz3BiFthGJb/W+18ivkDfkNVHEQCtsr9EmEAYKhkRudsloM5LYFXFJ3xaZHIq65UDETRFhWhspctr42M8vl8pWgBIMRv9AIE2XNmirTKcaGu3kijWvvIic1AzGytIlCs+r0skFCOdEQvVOWbYHXF2wJbDg42S9VsPkgNdZB9PrUyVCRif/+9pDKGYRh+GOmMs9baXzL//Xdba38suu9tYyJYSSCrH/ffUwIdlTuRUbnN/o2MZSWA8Q7VM8cUI4s8qpTO69f8GRUeynfLxMhCopAvkVcNLxafG1Oh0tryXRlIsxegx7g8hqHGD6D6TPh7Mi9wNlsZlBUjw8tuVVlX8VKZUen3dLQu4BpRSidLPak5x1xVzqLnjPEjS3f7y/J0IIqgeudEKc/o3dg6ZBWAlagRRsaPUyWlC/fQmBDXJ5+sLEq1obcFtiD/idBTFoHwuTJ/INDUqHdUvd5bGrs2IqattX/+LsIAYOV/6D7z0621//rd//9qa+3/bK39O9F9b9OIgLFweMgPQU+lA4RhxkgX3SMiZrKC/osv+N8ePOD8EdhXStk+fRp7J/a5beRRGSVo5tRzJhkCPQVnmc8xRTCbbdL8Pns2LietOC0yIV4lL1osYlIuW9XDeojY/aoU2tWVni8ftfLPZvkWKnvFDgUgHnt5GZmBYBUfB96toksy9tqsUZZdyx69hgoNdT/vrCi5FZZbDpufVWml6Flt2snueUSFsko3+iBZyMLnaRGunU43KTz9ffCi9jvVTcjyW2oy7W+rEihb8lQdKgfIePdvadxGieefba3903dVGn/t3b/99dbax+/+/wettV9+V+L5v7fW/kJ2z9syIhhqPWPTG4bYc+nZB71lbF5pMaGMsG/UpAm/62nXq1geO1Q0Lcrd9iiIag6XVWBEYfKHD5cG14MHK6GeUQV72l/8HoRl1A+BpYPYXmMVAZBX1jj1xpyv6wcGjO2diHukghforbJ4+3a3BoTdy3iON2/yPeX5N1S1HMNETCYrQ1vpM5XetMDqCGjPniXC42AfW+Wr1oqlETOHJ4u6MTk4n+dR0pcvY4r4HwwVxru64lUPvbzui8Vm/gkb9eCgtmkzj18dtP39zX/v7XGRWb/vKRpxZ8mmlPJrLeb1x3ejaEH2fTsuLzcP3XTKy7VwQemr0j0VrrZ7ynfv3GYoY2ysEdHTbt0Kzf395W/az1VC1VZxQillEcIII8IcgIy8CEPJhb29OJTPvqOcKryHKuu179CTjmEjOytjL28URKlF+9lIxrKowPHxcl+pyJ79PjMAJ5N16uvqQCqg0iI9Mriz3hYsAhvtq8zAr154rjCaFR1eWPGw3JX1HQmZqNsbjJVs8/pyqJ53yDaU2pjVe99y4y2MO2tERNiAigEX7Vl/0KKmO1HY+fp6GXq3//706eq7VshlXCQ+ghflMXsF3jBstmTOiNd6z1I1DO2xFRUlpgBzUZvpqORSPX8WHma/O5ttKgH/nSrOBRdaCqheJ/Y3ojRRJVoa8QmNvZRRwC40zspC6GPSHBlrp92TvZHlqoLOSL+2OXPDsAmo9bhBG9XMcC3sN/1ZXVuDnjxTTxoCP356mi+uF6IMx5CBdaJ3iOr/7QQrYZ1FIt4D/fWdNSKi+a828sm+H5VAY0Q5/8gTYGm2ihFbuafPmdp7sPuxv/VEFxF58a2/s/k/P+dCy3r3Z2e61weuqMTUvpPnOVBeoto/zPC0lPrDwNMSWf44iqqp6+io9g7RPq8Y27uORHznO6tuoplx4ssJ1b5XIOoKf4dV4JE878HMYW9XDEML6N8mMsB6VX33u7U1t0Zvz2969t4NXYkIwzZ1sqrJ1du3MRLWe4JeCCg6Xhami1D4PkzlBWoUCvLgKIBnPHHJNmQfhXFnjYhhqIGHxn5fARhR5lhR6sp7YkRO1Wdm9wSOgtXF25Ax0gW2lp7tUQ8kjK7pdBVJySpa7LzD2GH3RGShysJZVYYsVNyzf5SQt10dWWSlstZjGUcr76BkYObJ2/Xyss6mm5WRh5D30dGqhQFatlccTz9PrBKrNyVoL+uVVyozeojJVDfcyjtCV/amE23XbDW/vgoxmiOAvLP1Yff49t7b4UubqxqbG8XGUQxnHhMBrILK7yDXCTps9pssTKdaH7PFs55hT4dAi/zt6Wq45bjTRsQwrIxdFvavfh+9J3wpZeQpgURoGDYjZtjnitr25Ut+z1pOZwoAACAASURBVOPj/HlVhEDds5eYipFAqevjj/v3ecXbQk179dkrPTAig46llFQaK1ISrCkS5F62PyPOh+jCO3jGUh+2jrpaZgD6xWK5L774Yvm/rMwWBsN8vvwdnAHMY4+HraoPfKQtYn60HnJEtFaNRLSWGxFqb9sIXVZ6jvsoqvfpdL1de2/0AI429naU1kPRA5vfKOLz1bYYvt/WJ+JLbA41ydXNzwQMAGIMsOk3TzVvyFIJik9ALT57p6h5iw0ndZXAbDfuvBGBMQYLYA0QVCOAJKwaWrSVEbZVMbggcA/bF6NyPzZ8JZS9lKDsIWaqPJ8XSMrQtnPsS0qzvC9wEZXzzqirFcKdGTwQxjaSokow7TuxcLUyOm9u4v25TRhbRc2Yh6vKSnsjrs+f675HLJV2fl5XdvM5xx+xtApKu9m+tJFCtaermIjW4qotrC0zlg4ONstus72gMDt+r/ekTXA9fbq+nhFws9oGws/dj7Xr4Tfa+sP/Rns8/N1jwzZ2crL5IP7hKouWCf0xViwOyGy2GQFR3kUV2IScuNqYUVjzPhLxe2uoVEZrcfWEEljbKAIlAO3I7v/o0Wa0bTrdzTOp6+HDzd+cTFYpxR5yK3s9e9Z37i0JDvPgrMdtHQl1Tiuslmw9WGdFKMVI1vUA6qCsswoWixNRkdPM4dkGDzGfr8pUq9iAKIrI8CjR+Y2UsVpTGyXwNAUMX4Q9DoM166pZkUnW+M0AucPQh136o3+UfzZLiWW62keDv3awGH5nb33Dfb/Nh68dLFb3YJtrPs/7qQOcUuGfwILuirs8ygH35CNhJESlO9aQGBNi7xj3RsSIsVjk7Hg4OBn4C6HTbZDV9lJNoSogsbOzzWjbNjnWhw/z3DXLhysFbf+WnWtLfVx5VkRL2XpZoCwwCnAuGGETE6i2nh97g9GFs4imT5MyL7tqMLFeLur7MIYzQ0E5PMfH+fMAn7aNsfrsWa6kqvvg1auVQos66PpotAfEWkNEGQzHx7mRZcGhmUzyc+gZMVV6B9/D/48oztV1fLzZ1yTTWT76ah32Xzt5O3y/zYffaI+H77f58M32dj1KeXGxOXmMCEcdgIyookep95al+N/tbWLDOq2xC5N5X53xe8+IiMqLIRgzZLvfu7uKRLS2nlPGqORb8TkWboRXVg19IqVQQdGrd2ChZijjSt8SPIdvhXx83PdMOOes7baXHYqjxuMH2DxaICuIhpixykoGcd8s/cSqBJTCj/amT1l4h6cig1GZ0iNDmdGZRWkVmyXjZ2EGA9Y5avqV6aSx57tCfjcMMWCanWdFzoaoh8JIZc9Z1VmKaM/uua8dLIYfa9fDV9tifU5VgxI76SpXc3Q0DD/zM5vf9WmOTEkjzKRSB9ULh4DlniLgZsVoqW6eLce9EdE5omodtpf9fv8jfyTmdejx9lEerYjVbD7/+pq3Mu8xUntCnz0pHXaptt42jF55FhgdVrj1hNmRglSK6KOP1v/7wQMefXn9upZisdiPnlA6oiQVbhxG5BVFYNg+fvFic07t/6+sjcWeYW9mxh3b6xlerGpERNfxsTauP/ssf6axkcYPP6yd0Sya1LveGY147xrY+YqMRosNpDw3qgyGWdY9lptVuBlK9tGjTevMh2x7eCtev+ZWOjvMBwe6Pe2YRdnBuDci3o0qxibaWwwUxnLJV1ecLbIn7ArgJSJbSiCCgwGh2devxzFV4oxUBK9tm74N9bVP+1mejR75wASpvS/KTNVzwHNjf6/MhwUNZp/1wLdKL42eufDOWvQ9kPYxr5Vx7FjjJ4qIICXk08NocNYbGc4criz9WLmm0/V5QxheReb8M1XmOjpPlfRAVK5aeQb/2Z6zm0WDbConS1/5Kqc1uawalJyexj+chVCtlZhZwSzMBOtoDAhT4Re85T6drpdr+Q3kN3m2KDsa90bEoNH43stSnuGDB9yrV6H8yYTjeXqs/216ETx8WONkqHgO0RnL3keVf3sgmmL8rEY5bJhWheYVzsLm/v2zPniwuxRUa5u9DKLywtaW+fvz82V6je1LtDG3e8UaYlXvuBJVsNiNiPIcUVrmfMFoef68b94qNPNjI2L2Oj7WYfjsmWB4KNDtxUV+pjOdwAD+WdUf9gmLimYkba3VDJyxqRz6vsoLzzpoRmUoyFdZoVzhhMdEWTDM8XF/50HWHS6aNBalUIbIexh33ohga4WqBFtqmQlH5u1WPCp7UHpDiPZi5GmVSxkSNuwZpeAODlYepd+70fvs7y/PveLIUGtlz9j5eR3bAP6XCCQYcSHYNYViV3OC/fP4sTaUoOCRWkUENKr8iC6vgIBJiTBku8Th+CtTQFFvmG08YGV0VivooguGUu8zeSfFkyfCAcmi1FEnUiXLWsur/vxcqQgYOgz3pkPZmZvP1/cs6168EY1XL/jJJzWBwb7LhDoW0LZ4ns2G4dNP140Vdc8xFNx+EiMLn9XOQujusilScdx5I6I3V6m8BV9bXhXOHs8zNvzf2qbXWblYSWg1/ItKEC+4bQRDAdU8b0ImjKwgBnNmr1JADr4XJGhHhguxZdwRABSspZg7L3cmk+2U3rNnen8zumEYPNuG/auXwryoi8ll5hR66oDe9Nfe3tKZZL93eBgbrcwrV5EvjwWxbepV6ssaAqoyMSpMsN/3HXy9TGS/v7+/3Le9OkrNQeZkWWP38nIY/v7p9fC7R0EjFyt4bNkHJspudqQFWHjZC2V2L0xUlVo0eknFGBZFIjwQyS7+LdNc+3HnjYjFos9wrOSoewwTvx/OzmrP88EH9WeOLobgrkZEmFDzee4XL5Zzdni4EtC9abpdecxgZ1SlaFYGKaNGoeBPT3nKRWG0bLhbzfe25ekoM4yMJv/etxWZYHsH7MGVPeodr0qFRGvrJE9Wh9iOrwcHy2qE09OVclSdaZUzq7zyMeWx3sDAO79+HUfK7Fwwgi78bsZ6GUECLL6qR0exiKOfF8ZhYg1DxmS5ttCRFewtEoTpImKYYYjDk8pLOjqqlbeAWjeaNB/6VJZf5aDf0rg3Irb0/tUerQrjk5PN+vHK82SGRtUwQl7fCgal1B48WO5nlIVWQu5WKI7dz5lRhnbG/nz6eYw4F5QR7w0LFclQXVqVATSbrUdx2HsdH2+3NxFlyqIrdjAcxtgS+GhPwNispKNgCHjHy+qDCMzpwaoe68T4UYaBd3HtSb+p9YesyKJE9nkzzI4fLDUCzElF11Q6a/fqqCy74GUFMwy/2d4Ov9Vmw5e9m85zSODH5/N1i9IeEFWKZ9MJimXLe4MPHuico5pEW3Jlm8ewQ1zZTLc07rwR0ZMrVTlRRNOsIgKWwnoRTDiP8f4mk9xLhcIfI+BZr5jWNiubKhGXzNhWo4oxwjwyZ8K3UfeGlTX8mECDkWTljVWA1qONvDMlkG2ZOWt+xvAMuHwkSmEQoORYuinCnlhnjXnFT57091VBBFnteXW/6XQY3ryJQadRqXO0/7K+SGyuKuk3O5QRV3UeK5Ft+1lF8gXyRX8vpmsq0b9tdVRm3Kq0yh9qN8Nvtc4wncpl2g3q+5JHk84OZuRdWaATykABtmNey9VVnBZhC38fifjhRSKqSnx/f1PYA/nP7mP3JaNwVim57GJetjoXPfe1giErF+uZO1bCje8zYczCrSoUDaU+hh4b6Q3FSaOUGuRRFgm17xmtBeQOFC3mKzLSEL3F573BhAslvvCyfbop86T9e9j0cJUReDZbNd9Sxic4d7IocLS2TOZaci2WQlbPb/k6diGH1b0shiHCKETOi73XmDOvdE3GidOjo1gEKDNoo3PTHZF48SL3emyOUX0WTH5jm1+pULUtWaoIVdYD5L4644djRAzD6iBjwyqLnQm0qFwuyn1CcDJWQkQ8ItbCn/u5fJ95z7tSsmUFAwvn2gGlYn8HUbdM4Kj0Qdaa2QufKL2QrR+4Dpi3EwE3sa49EcSM5Mc2csN8REYaA5SPLfuF0VKJUPRGzdicqyqBKPLi76HYTNFRFykuvJfHxmVG5mef8f25i+HnOcMoKH6lq6v1e1ZTXwx7oIYCEqvvMVwRA0VX5lXJF0R4/6PZzfA702JEIotEYGJsuI4peuUxWgGX/X0s8xi7nxUs2Ni7snyL496IeDcquW+1jvh+T+7TKwRvQNrnUeHJb32LR0dwwbCNjBH0a2ACxYfB7Yg4XJiQzzoe4owzgWX7TvjB0lGPH2tqcguojIRu1HwMRkql+6XfY8y4YdFR3IelQpgx8vBhf8dVtgcj4c72sVVIVSPGKvGsEZj6fsRmapW04nWISkwxH2zNt5XN3niuNFtkkYj5fP1M9JSH46xVdY2v4Hn+nBPlHR+vDHP8TnbOoiiInafjY1799Wsnb4cvvQeIDpr+gFxerm6sQizWio/yLVkIKfruNta4Z+JiedD3aEAMwzDcGxHBUBTtuBSFcCX36e/DOO4zlkgYxtfXy1Jp+7cXL1a/rYiybI8P9dtMqWTvw1IBmSH++HHMB6P4LFTkghlecDQwH5ESsdEBvAsMMetJofrEg/KiUUGqR50wWZUAM0S2uVRaRhl/EOqVZ2BU5JV9hWsy2cQY+bLh7H7VHkb+uVVELgrJR9geZswwcGVmaGRGBKtG6hkwaOE4WL3pS2t7rioeI4pkfu1gMfyPJwUP0Crfy8tariZa3EoIydfD2tRDL6jIRxnUop+e3kci/PW+jQjlMTJhxixyLxhPTvqt8YpAhTD2h3g6rQlUy+SYfbYnGqc8zez+kRJic6QiF4wNEefQrktFhli+mb29TW/bpkR8FClSKh6F7p/XPiszTtW/7cqQyNIybF2rzdaU92kVFbAvqpQZ2AgfKbNzH+1Tu0d7G8TZ54+qenw3UNb4LTO4K/M+DDEjp2XUHVsppeSROmvVi1GWZ2lCJT/WIkXqMLDFixqJqMOcCUm2MfBM8DhYzS7b6Aq4pIyIw8MVivk9GBP3RoQb0b5Sh0BZ9mof+66A1dCxv2AEKOpoJYiw9/H/e6uFlPKudATFUHiLqJLBR33UM7CmeK1tUhErhkCLEegVkFFaIIrueENwf3/T8KpUCSwWNdpoAC5VqssrMoZH8Z4h2+tg5VTvxebGyr/LSx2JOzhYpq0seDlLFfgzqxyGCC8TYZ2Aj6sac5nBbYc6T5XGePZ3xuA8VBXb3l6tc6xaQ0ZZPtaJ2YgUMasWCF5rdSqEtJ0wr5THEIB4kJpFCWPx/WdQwqcMmSwENDb01DHujQgzxqaqeiMJPn2hlEH2LPDE2N8OD7knmVE7q9+GwaIMEeYVsvm1IGIfFsVnMgdCfQafq2AVfGoUKQIvJ7alSrZR0eiZ2Dspj53NqV+/TIn50s9IkUXGT7RXffSY7Q2lxLHfFKjQX6yJGlPQyjljnn6kX7JIR3VvVAzuaGQVFLhAs967v+w6KbxSxklzdpaX0voRgboz2fiD91IfVC2U7QZQFqjdHCqcyvKyEYkJFp/lnAE6iihKWY372IUeMe68EWHDy1FOPrpY6DcLpcKDirwDXzViD9/r18vfUABCha9hIK2Dg83n9yWprS2FgBcY3rjI6HjZ/DIFH3nlKlqB6ivrlVbTKSy1E6U84PVkjkC1koO9k0opeGPMl2tmOWrMN/PcK8asXy/2bhV+kCzqh/Ucy9yZRaTVvFZTCWOdjsr8VJ55m9+P9pcaisUz2mtwZth3IaP8u1rM4t7esuxXrUnW0rxL8PTkwpiQQf10DxW2Z0LLFlR5rFH721smnbrTRgSMOCjLjJwJRmF1Xdl+YHn1yr4GL4E3PA4OuCeggIjKs2MKtMJ6iahKpGiycKsCV11eroero3n1Lc8jbEJPaaYCbvoQepYWiJRxFn2x7xHJRCXUQU5mGzFVOS4qc1UxNPyoREvwPmP7eezSAYsMjDFGTvRsFeNuGHSkbDJZ6TPWQ8PKot758VhCBgr276nOv6Uzz1JQCjhb2seLBfcQI+WahZI9R0NWzjedbh5MZkX5Uhh/z+iZGWvdrg8CGXfWiKikk9SBUL0X/PDVHR99lAvOzPtkexUYCzSbUwYEzhJD+/vf7OmfwSohbJ+KTAmoPc6EqYoWecMsOjdVpQch9fJlzpfBZEAWMcXflNPDKNHHKtTj4/XoBfPgbP+X3rnKgOp+rlTZMruq72y7p0bPsOuhlCQMupcvl+9bkRk9EfioWzV0UxRd7akGtHvcFh1EuhYRRGXssO7AOGdj5EQ4t2Ms3QjUZulcMTnVci9WRsq8n54actzn8HBF31rp076DcWeNiN6228DAYGThRhUyz0BIbI9YUO/+PjdOWYmov0fkwb5+3Tc/ltskAo9W7sHywko4MeVXKZNT86GacJ2dbXaEtLXqbL0zjItCxy8Wm4pyOuV9DsZeMICz+zEDNEsNwahmGJeePbjN5bun3qLjFb4bGI09sRsI7GwDOhipdk9VKp+i89HaOnaw6lBX3k2RRfn9gXOSVVweH/Oyc2U0RnwxpXUvWRtuqB4Angzj6dN4gzISk8ywweHKnpkJkNaWm/DVq/wdtxz3RkTxAvAuQ8xjMGGQtT9WXm4FgLuL3Kk3ktTvzuerNIOi7c6Ihw4O1kHSVsHs7w/Dd76TKxsbnu91Mtj6VZScDePa70VcERVgIksdVQyx6gUejgwIqOaN7XW8V+Ue2+bvW+NzNJut6LQr63ybRgaMgiy9cXa2iTmyRlA0TxHGhu3TqPTXpuWid4qeh6XchmFzz9v0CgxNpUMV9flOovK9G2Ab9KytT2ZlSVGuUJUrsaGAcbiePt1uzpJxZ42ISElWMAv+kLDWxOyAnJ3x+yuglTJ2ooZuflTPAbo+YkD4YJ5gSPn+CyzVlxkA3uDuVTCWqh7PWjHYI/6G3mcA/wur3IrezQvDSsdEe2/7nmdnq0hANt+VSITCp/RUD/UCjVurd53119HRZnqaGTq2KZ4iUNuFoVFZS8vq6PeTlS1qz2URBrbun322LneQos/KPbN18+dQ7Y35fBlZ89xL9tzaKMd0uq6DfSR49Ohd3Er9rJqYShmcF57TqU5jsDAmQ8Czy3Kk73jcWSNiGJbzb4UXNqovY/QCUhFR+fpzhp1QQCxlZUf0zVHo2I6qwLEC2X7XhuHZ/vZG0c/+rD53qBm3zx21cW6tD8yqSgmznP1YhyMDXY8hzlEyiaVM8b+np7qfhP2ej456GWbbA7AKkAzHEa1N9J7Hx+PSHL7duU8tV7zoLFxvR0RCWNU3rHU91gr7QhF3WV4FW8Wwvz8M3/725nfm85qOic5Ttj/9mWJ7Yz7XlYoqgnNwMAzf/e4mkHN0NCIKGTIrEmRQY+g4WY7Ve4oqDcHyPBD4Nme4WNRDlYyBcEfjzhsRACRCsVmBwMJqwNRUmPB8lEIJtYiwKku7VEN8WTld9V5VZZudO4RvI6+LXSyt5N+xp6kXRs95rFyQFcors+Xh2Xwyb88bumy+9/dXoX4VHfVlxFA6qgGZDV8rkjMVBVLlmkdHmlQKHWuVco7C4lmH3MghYPvEA6VfvFhPgVUa3GGOokgE5svPr6+mWCyWEQbolrHU05gL60CwCI6NFjDwo90b2ZmuRONU+pcxQKuBM/brN8GEMiuyJ/qwt7fsO+BDhJmwv77W3f8qwuinfqpvkXeSD9ocd9aIYBsdZYJHRzq8urcXh4UfPuRRLHgwbM8gXabCxpFwqNTj23ux6ozWNtsK98zb2Ctisou+00PVfXXFf4NVIkShaAjSyjM+eLCep1ch20jWRGc/83jxNxgZEWZksVg+a1VmWu4F1n2WrY1VtHt7m2cL54NFdi8vl2uo6M2HQXOfVAyEi4vYsMb7qtLo3jSMNZ6j3h9sfm01hcI5+KuHOTNKwfkGl6piEgBvD0xW8xrJlCwtClmbAXm/8pVh+HP7l7xt+MXF7gTa06ccGKImO+Iq//rXly83Ns+XTfoOx501IsaGr0GeEnnQzIgAOlvdF3lSFu7L8qzqIFVz2aqHhhqeG2EbD6j3Us2bVAhVPRvC4D6KGcmT2WwYnjxZpaiykkurGBCyjdh11X18CLtCt++fmwl8W3FWnX/IvyrXhprTvb28g6d9RtyDpfGUgn/9en0ubBvp+XyF7am87/n5bvavV9Yq/RbNb48hr2gDPvxw/d/QsG8YeHqxwg1iZVim++w8KFl8fFx/T1v1wp7vzzRhRPzCL9TzaJUIhRekLC8Fa2uXoU9cUTjsPhKx27GNRw0BdnOjGwRte/nQZuVZrWCNKgLGVDqx+YNAiwzqMe/95k3cL4Hl6XvX02Jf7H2AnchotT0vhKptt+sYKYbPPuPft95n9R29AmBNnjKmXH+xvigqumGHKp/f389JxFi3UmbwqkiEf+f9/WVUIyo73NvbNHBw1nexv6vOIEuvRQacuqCIYfSenMT0A2/fcsObra2XIxVngnVCjfZST7ozwmV8tS2G324iX1ZdPCs01Gd+9mdzr+3gQB/4bS9smtlsaTWzzbzjcWeNiGGo4QTUZoUXwf6OdvaKdKx6eQ80C6cjxVcR8JEXNGZA+fpQ+vFxX3oR78yEme1Xw97N56yZUJtOlx4qmyNUPkDpvny5uTdY+gieqgI2RmFbGCVqj1jDsKI88A7+N3wPiSdP+PfBRWLTsgrEm/FHRGBDBuL194tapPv5Z6RFiuBIRT6wtiyCNwyb+yu7vvWtWodONqJ0R9WYtPIgi9pl+BDFkYP/n+FPMPdK3kR7STUZZFeEy/jPJm+H39mbD1/OyUFtbcWznW3+LIpgO/gp0pldpinU4l9d6c28w3GnjYhh0GHm6IIgi4wIi5yP7g0Pj+0pK3BubmrALeQkM+GbcReMnUtPqNTjwfkSU6yNpb5mXud8XkORt7byhDK6XsgC5ZUxrgf2+76bKhOWUTi38huYO9yP/YY1GtWetHnvSqM2u+bsHTHXz57Fe1vdrxrtYAY2a8hl79FDBmh/pyL7J5NVRd2YqF/23t7A3ttbGoX22SaTmLlWnSHmUNlmfkpuVAybjK5A6bueyIuVcx403NoyIvGXH5wP/9+BszBRhQEr+vg47p5ZySkC1IGoQFUQ9lzzub53Fei25bjzRgRGT62+tXaZoPJpBdZPAd4h9ij7/fl8hb+oevNQApEQqgpnfDbiVri+5vXf1kOpRmI+/DBfJ2WUXFxsep5ZE6rMcIRjwv5mFS7e9+RkU7izUrZKPxC1Hsob9mF+u26+sk0ZUDbyVcU8sD3BAIGolrNkQ+r7DJumlHCkvFQK+/HjpY6wsle1KLe/U/WGPbMi89wjY4XNPVgoGcjU4ntevlxVT0RGizI0lXF5dbUsI44MS3tPZmx5gzoamTGpehD5dhSvXm1+5qttMXy/deaH/dhlDrdy/fiP88nPUNG3hIOw496IeDcqljQ7mN4rQDkuFAZLh7GQnlKOPdTHtgRMCQkVemQKooKr8ILVlr3hez2RuwzgqfLfvSlG2/xH4RmQllL3QK8ShK2PjpbPwuixMzR+lSxL7YWo5wpLC7H+Kdbx6jFs7FDROTSOi7g6Ii9XKd7IS338mMtYVZoavVsPw6032FnjPO9EVNY52osnJ1yvKdA0S2eqFOJP/qT+3YcPlxgm20sDMoalk3x0jQ22D2x0CxkHdm5tyjPCS/7ne2ccaOknz4dG7YIp5sDKNZ1ukhSp0Nne3nKCWV/7Sh7Jege3MO6NCDOUl4fQoDrwXiADpZy2qTVDKceIqhglqYpu2Xuj9mB6YcEwE0qJZAbXNqDj8/N4jdhvZ5UvkXwAnoEJHEW/m12VucQ8RTKK7ZEKwZO9j1J+FnA3n2+ykKq0SDRubpZgd/Z7X3wRd1uspk8q+8F/v1JNxEp+7agaEQ8erPOTZDomM6h6CgeUDvJRbaak2Tzu7w/D977Xt/dR5aGiGq3FDr6SO+jRk/UeyloL4Prx/evhdx8mk2s7E0YW7ulpvzGB1rqWpCgCbVqOf7AYKmGeCZodj3sj4t1gm3c6XVrZURiyt1Q0Shuww6NAdx67E+0R9W7s8EfvBfBV1BkQz9ZznuylQvJ2WKUwFqPkgWLb4CzYebcN0a6vuWDzoMsx62j3gp0byBfVLRM8FqpSwRqMFQBuBjpUoNPLS52uQzov2wtehkZ9bpSHDI89St15Ja30xs1Nf7SbGYFXV8Pw+ed14He0VyMHAHudnffPPx9/hlWKeDLhBu8waMBrNZWkALX2mk6H4VfOCqFnvIyycC2AqHeSogWCkcBCLaxkCRbko0d8U2YW8pbj3oh4N6IccBSGraRB/HpX8pSMVdBGsXoMy4qh440bRtKECEt2SMdQzbe2BIdBqCi6ZTvvvUoeEYtKp0pVCre/nxstSBfg2V+/1s/DokTR+kZ7gck65Xnb/RXt/QoAV8nQijGZ8enc3GjPuSddaPcN2zPPnuWpFA8Y/fRT/swMO5Bdfr7xjD0GeVS9FTXuevRo+cwsxXV11X+OEU1khhcuGI+ViEjlQqpZca6AmGqNT8IeJrYRkSdVFoxFabMfPTxclVlmL8Aosb/9bf45hX6dzZbChm2anTQe4ePeiHg3lIXOFIBXuL310lGYFoYoO1xjK3UqBxP54/PzJYOrF06V92pt+ZmTk34mSih3hVFgc8ZSQOp69arm6ftIIcL8lm0yE+xeFql0C5R4Fl1gz8kqIhSI0AM+/e+ostlqBYMiYnr2bLu234p1MkoXPny43MfRWttUAeSuCqFH57AH5Gsvtb+zBmnR+bNYADYvWSoS3XNtBRjApr2lrbayUKUEGVGkTz8prJK/FFGkZaCW+8GG4/wEV0mAWHTAU3z6RkoKeWpzYey3Ms6AqtLa4bg3Isxgm48JZh8d8iFfb+D6NY9Q7mMBbb3v5s9LVj765k2t5TeEoUJ5K0HIBLmfM5siGAYtxF+9WlcSVSM8SimpMmDsDxgKrIU5I3vCmlZxDv457TxkuICbcV+eRQAAIABJREFUm9ioswqzwiLp924ECmb8DVle2z5XBTemvqsiJ34OVTVEBaPB+mkobgwoehtpq5T6QuaoCIfFPPhIHsOz9Chp6CQY0NnnJ5MV3gZ9WryMANFY1pguS5tG69LtdEVhk+yy1KqVNsJnZ3n9sQplnZzEBEePH2tO8ltKadwbEW544aLyp97qVWFQFRJ/86af7lY9Z+Vd/H97Qyc7JyzcCcFYEYaI1rE86eHhMvcaCTX8jp1nxRlh18+/e5T3juZehYGBSoejoZpWPX26/m8WgKYMAEtzjP+1qTWkJJSitcRKkTBmv6OeTRk2qjmVr0ip9AqxmIax4W31vOzcsN+oNGHEsJ09fToC6WpPy6zOp3pXYDY894HlB8nOv/9bRUmPTU36s4vIEZ61AqStrv1O9GMvuI09+DbAJvsyamGs4lH5PBgh3uKz1Lc7HvdGBBmRAdDayrOtClkvWPzaZhgLlT6J8tTZZ2z05PQ0PydQlGzP+whB9A6LRezRs4s16uoJt/v5V15q9tw9f2tthaEBR4J6TgXKRkoW6xilJPz8zGYr8GQmtzCXzMiqVmjAuQKdtjIWjo9XSPtI6TAK9x56ZaZgKiXLWRPGLLrBvtPD+eP3Krx4u2e3IQKrPG/1ms+XxmKW3vMyguE+1LxWUimZDi9FJXomAyyWrH4+U9SZsRJ1eIzAXNZCY6kQ3wJ2h+PeiHDDCxrkxG3+NAqD+pCczZ9GEawIY1E1MiLjhymtDPiHC4DHHs80eoce5DqUYQ/o1c57FupXBod/bpvW9CW1l5cc0IjSbpb+ZA2NPBV1T9WY9fZQR8/KNQHgtpT6T57ERlYmHxU/gaoqgJLGfFbWxkfRqoBDSz6U7V3/nup3lNIak5piA3tNVaxUeF4qjgbb754TIjJcT09XzkhUQWLfXUV9qp152XPY/e3ftzoPw9u3mzndr39dCyXWQCfy2KxAysAtuCdjrlObFEJJ5eAZz/yOxr0RYYYSNNgvjCxGCSaGuFcH7fBwqXCysOswaMPFgjEjHIZ6Rx9u/+STJfrcdxZlhm80n+odlBJg5FXqmS2pDLAPbN6jPDM7V+ycWiXrKaZVFCUiCmMMk9t0Q53PlwqT4Q2Y0osUVY/iWyx0nj57Xiggthc866Nfm6yFt5fJLKUTEXRZng3/O48eDcPz55tnI1J6Wci9aviqHheZoobx4QnFbPQpA3b6K4q0YQ0tJkmlUFSa6Ppar/FstgImR3K75PSo8Cjr4tbaOn93Zp16gRThIexCsfv6nC5TQKrUyRNn7XDcGxFmRJGFTJH5yBb7bCRYFemMH+zelY6M6McSvaPN7Ubvy7zxntFTVu2NsijcrEDSkWDMQJdZJEPN+/7+0lNTIEJUvNhoRnVOeq+eFt3Z9/zI8BbZvSP57Y1qX7VUMbpsxErtLTuYzK8oVo9ZqPyW+s3I8LXnQTGgqqol2xwPQElrgDPZAD2KNYq669rz9vTpeoTQRnTVe1XSi3gGa4ArDNYXX/Au3D4C+I/Pr4ffPRSlPoxoxS5mr9KoEFlE3PS998J1X+L5w41EKI9EAdKiaEEm+FRozw6vUFVHxtY2q5RQD58JOAUkHNuV0A5FQgPFqg69nWclONgaQflEoWk1ohC1Ktm2siDjlLD7qyIL7IWURMbY6b3U6+ta1UM1EhEprGhurLPGqoNev179fSyBmfJImVxV5x+edhb5APbBpr6inh9R6lEZVjbFpBhAx3IfqVJXG6nIwJizWR9VP3t+n7qKupleX/N+IpU9DTn6B48Ww/ebEA6MncwLJSVQq0JUPWi26cF2md3r5cv4EG857o0IN1hOPMuN2qFCtPaAoAnT6WncrjgaVgj1ClgIi94+Dczw7UVGK88TnQ9L4cdBEyup7yOU6itAmGdSRcxXiKeyv1tDlMkDJSOm02H45V9efldhWnx0y3u8kUFbBQP61C1arWdK5Ph4Payu9vAnn4xTSDbdpmS537fMUYAnfnRUw6gwgy2KdqjUo68Y9ARkWSXRmDmzXC2R8RPJGxQXVAod/NnwaVkb2WV9Pubz1XtWdKl9H3+uv9neDr/d9oYvWxu+bG34121v+AdPz2pgmghIpcK5mSFhJyP6XGVTslzRDse9EUGGz09mXgGGFQ4IF45tqFT18MdUJgF/kSG3vTcVYUCq83p+zj06iyfKDBx8xgsO2/yrF5Rq7+uZI/HvY8rdWMdI9fss5K5wDrh+4if4HrIAYPXuqsFY1BHU/jczYBFhyMCz02kNL9RanfbZzqntlFrVA9vQtdv3V0Y1lGGmF5hHzu4VGcxjjAgYVplsiDoeI3IxZi6Z860ctd7387gLJje/2hbDf9GOh99q+8NvtKPh+20+/ObZ23WhglQDyGPsJossRi+QIi4IO5FRTrR63WIqYxiG4d6IeDfUHohC7xUFlfUcUMC8+bzm4Y85UNV0CaNhrpb8qXuqUKgFD/cKzx7h2+M0QCmgamoM8BHdMdm9/fwxfAEjPfKXlzHMy1bAQnB3qDVV1Upf+Qo3jKBEe7ASGaanZ95ns/5mYlFKZowyRhrGh+Xnc80m6SsG2b73e5pxc2DN7JxNJssr89YzynAMpf9spUS1z4idAwYDABdLFoXJLm+MsDVnLcL/zcwIFRwUZo1HZZ4VA8N7nRmIJDoA2cvveNx5I8LuDUYYFQkRuzZZuWc0FD99puwx7F5EeZ96ZlQ7MM+y6rVVz0qU91VzmXlBkQBR+Ak/7HNFGAsrHMc0+WptubcUfsNHGdXcf/xx/BuMNdS/N4sMeGZeP19jPVoAc6veKCK3ao6R0oCsjYwqsJVGe8tzYTCDB/TZ0furc2bTAmBtzAD5EQmaKmNm7xkZrKrT5+Hh6m9Zm3I8iwVpwgC4uVnOWS/xI86C2m8+Lde7L7OIJvT2fzK5Hv5VWz+ov3sUgCT9ZvDlOkwQZcK3F+TBNl+Ws93xuNNGRIZ1yLypKr4mG9fXmwJpOu3HGiC6ZhkUAbx7/pw3M/JeG/MGKnswui8D/s1mS2FjBUSlpjs6ywil26hH1nCrgsIfW3pp241X9warQsl+H4ozymOzd/NcEn6M8fhms1U1RNXwskr+p36K/71ahphxcrA9FlVuRM6i6pAa0bvbq1ImrZ5NcUVU8Qj2WZWx5JW34gOBXBnLGm3PguUzqXwO8hvRHP8eqnzUng3o8F8524xErCmD3nbNvgb96dOaYOoxIKbT9U2ZMdvdwrizRkSkjCzYraeOfmyoX6Gpo0iEN2iZcPSeVyUiwMCJEBRRBKLXY/Xe1xhFy6KKyhiotP6ulvOx62tf2zzbLC1Q2Rt2nrOqjQ8/XH1HteyuyD871z0RJLZ/IvIyeOV7eyugul0bxg3gjdixbbarYFy2X7yzuFhsNqrrnacsdaDkz6NHMeNxtmb7+/WeHfa+Pc/SMw/M6K20f6jINyVDlCz7zbO3w7+ZzYd/ffh4+HKb8Ee1CsPmvrKJZFYa8qWXlyt6W9wD/39MHX7HuLNGRHRw7MZTAkt5fEqQZ8/C9s7z57ES7SW9quR4WUkkogbKcx1rpFfKYlXlBOaaNXhieWdLMhcx/iG9ZaM4Fa9yPl9GIU9PV3TTfmSpGjaUEfFzP7f8PbUnfM4/8xI9PoJ1Mc3mAnTVkezEOuBz3pCoGJM9eIvWlhED5eA9fLiJKVHkfvZ8j2mRbedJRbvtUO+JCBeLWiEKFK2T73J6cxM34MvaOWSMleqKogRjI7t2X6msQhSpfPt2GL52sBj+1MPr4WsHi3UZ34Ow7sl/IkKR1YufnuoadtVLoJoT32LcWSNCGZbMOGBNjxRGJqNX7c09M4XAIgUKNDcmQrBY5FTY3nOt/s7h4VKoe8KqTGiw+WWGx9ERF6Ao1VPljV5AWS+nEqYdk3asGBWLhX6fyEnyeIfMEFJYA9ssjnl6CIfjtzIFD8URef9Z1CbCWyiwpwL2MVlv0yswGrxi7qEkV/fPZIZ6TxYl8Wy6ar2nUx49zZ434trowb9EZ86P3siuTYXs76/zjGRzg/fw7/jvzRbDv7x0nsvFxeYLo3FM1Op7m0stgvX2/HXLWAiMO2tEDAOv3PEhy2HIIwxVqzkSGlnZVOSxq7bFzOOGIa06ZuIwVcqY7f70Bx4eLPuuJ8DKyjvV/KozlRlA7MxHAqp6PxWBiPYegHfMMLWfzbA7LBKEnHvGgBgpHft+WZWDWiu2LytNCseUGT54UJffDx5wAxH06WNz/H5v+7N2dJRTV2Pd7TNMJjyN3mPE26qyyvessRp58IzwLps/VJOo0RPZVe/y6lUtcICIij0nf6G9Hb7f5sNvzb6yGYq1ITocBGzaKid79kBYAHt/X3efHe4IsbujcaeNiGHIsQWsXMyPaig+EhqRNV8BcD57tnlAI+XLwpOHh6tue9kZYEYSM74U+MxfCGsy5RHNrwrpvnq1PPPg7/fzwLqPRr/PBBGo7P2/KUEf4T8wpwpMysrFM6IqqwiUslANzqI1zxS8B73ZuQGKnz1vxFPA9lZEOV4trff36MnxR8YKQIlRN9OseV81nN+bTrSpveh7P/qj/Ix7xa7WYm8vTpN4+ZdhvKLRm+Ji62XTo6zcc2Pj2BCc3/zqOxUgDcKIUZOvqHEIJreivHYw7rwRYUfFMlfKMzMQmNL2uVeFv7AUwdYYhadZwUR4g1k1PooawbVWQ5TbUT3cGYI6m18b0sVnkcJgDIosXagElxKSwIqw92GtrHt6I/jvsjm0Sj2KJCBtyta0J+2FVETFsbHpoMvLVQoLLc1ZOsDuZcbx4NdFRSMOD8dXyCFSUnEk5/NlqocZIpbbQJXXMmKlCm6ncj4QaYsaWGVAYtazSaUVxyhwcIr4CIei387SftUUEzsruD/21I+1zXJPeiAqggI/CnQ6K8WzAr0S3oNS8NEJS4bVO4kjx70RYUbFomcH+e3bTYt7MlmVj0W8+xZQdnrKP3N8vPodqyTRGCcry7RWvhUCirZ5Pl968krA9uzDimGGds32WT0hHKuVr/6OVU62JCxLmVhDgyksYDoiAazOv3pWu24KEe/noIKuXyx4WsYbm5Ey8KXwiktgzB6A8crkXkQhz+Z/f38YvvWt+PfsOnmip0qO3/ILZQYqU7Lz+brS29tbtWRHiivD7djhnQXL26AMqgpt+8lJvI5KVlQv1WfDP3OlC2q1FPvsTMsTvGMaiWALE+Wk8QLMQp3Pl4uhuhqqA243jI1O4DtssW4BI3FvRJiRhYWtgLDKTm3eyqaezVZemgrBHh/HgjjqGeHfr+Jxzufr3A42Lefvx0rf/PDGD+YFSsnnXP0zgm0vKq+OFKntUqpKqNX30UOi6k3iQmhepWIUoNoqdVVSx9rGs3W1rZjVZyw9toqYtbYqR/f/fni4rnxZGiJr2mQjHNWmapb3wZ/ZHpCf9f7tcyt9MJksu0NaGTDGQO29PEOukl/YV4j4sKZ2PZeVI2x9qnPNCLfm83xvsOdgoxoNsS3mlcyCHPpLB2+H32qz4cvsppVwHqzuyoT5l61Ytf57Y3gDRo57I8KMyJqF1wCjEW10xxIR9R7kqOsiOtb6igc/VClpdmWhf892x35bedW282H12ZSBpNYiMhSirr1WALK/AYAXhUejVAyEPks3RVGVyFDDfXwr5pOTTSG7v79J+KV+O1NGiMiyNEQm3LO5yvopLBZ9TIkPHqxKACNmRvZdYOv8ns84frYFatqUpn1vjxPZ1ljxV4bT6Hl+FpF780ZXH9koCfA0ypBg66XOZYQ1tM7h9fUw/IurpMcFbqoENA6Oyh0pwJa3dCrgMst3z4R91Nhli3FvRLwbFY/ph3XB0M1q9AEkjBR55fe8sKuARP2Z8gc04+WotKb28+EFqErNVKo8rq+Xipf9HvOGfa8PT01tkeeVioaMMwPy5vXr5T5lDoUVgP49K8Yu8FyvX29fmcCUP+YNCjjq1eG76Ebzl+0v/45Yb4a/wDyy949C/1GH2wiD1CMDWDVUVvIczUPPnsDe9GdEzQne1UYxlcHNrr29uD+H3/fKyD87W+nxg4MlAF2lRVEFBUcMBuZvnrkNqCoz/EPYki22OPP5MqzlJ8WXq2GRK2VHPYQrOxr3RsRQ95h6LtXDYkx9OQRfT9RDKfJMkAFnEd0rSv0xgTcMseHRy2mBqggrQBUp08UFX+uePjcAqak5qZzXKN3jh8qze2D3kyf8fr1ofT+39n/t1VP6zgyvhw+H4fPPN9lPmUddqZqp7C+mzLI1U3spqvhQZdYwVLat+Kvstx6G0TdvdMoM7zqZrFc1KiPbX0iRWSZJZdxG+1CdSX+22H6HU47z/vBhHjFkf4ex8StnS76If3i5WP4225A+H2vzWmqDqlp7hi7t3Si9RBsjx503InYZAgSjHzAMrK4aodcegwBNnHoFkQVF4V0jI6bCBVBJz6HmWuUa1b5XpYH2QKvc6sUF/w5rcmV7jFTW3qaw2Jwo7g6PXegZvkOjqgzr8cze5xVFIuz8RdwDvUOV+7LwNcO3wfhVeylrogWDwf5+tA5wNLzhBjnSs99syTMMpslEG35II97cbMqEBw/q8gnYKTCP+hb0dn2BgarcN+peWy2fr/SxgrGR0cvDcUn3qeJWtwKuIsiRZ+w9eBHN7y2NO29EsAN5eDgM3/xmvKGYEGGKk62h8hS//W3tHVWxNX4f2rC3srYZUZLae+rZfXWKN8Jxr7OzdaE1nW4y8J2fb54zAAoVSQ9L96CqKiq17jmn0RozZaEqSdjwnrm/XxQFYFEnBVIdcwGgGX3mww91GkI1U4pYELNxc7NJMW4NxEhmRsasSuWA/wPvqFIydh3VWUHKEVEwzC+rxqjut9lsqTRPTjaZNRVXA9Zgm9SV5Zzw6aFtetFE34/2u40wVkmmouhTdNF9qhCe8OgqHfVaWx6aMayXt5SyiMadNyJU/pOFsFtb9bPISg79b1gFEdH+RlEApoDhragIAzyOYdBC7eXL7UPtEfGPBdwpA8xHO5QxpXAdV1eb3vvXvx7/doYx8c8QGfkVPgc1engk2KWIsxSYtbUlaygwNFF0CpT9b97EzzCbDcP3vreJ11BYI0RqMuZKNvw6TyZ1Xp0o7aHC9Z5iPKtIirAplkcoU7BRbwlV8cSu6ZTLuKMj3o6h54pS8BEzrpcXYA9lRpknaYzWFvNedbgQNe5t6tbaemn6D0bUbKk3nxMZEXt7w/BX/2rewvc9jHsjQnjn2aHBdzPl66sYJpPl4c04+1W67ehouXmPj9e5FKKDY++r9rCNHGSD1aSPzcH7Z1S/YQ0h9g4KgzL2YqBplm70XVMr3Qf9/mOKpseDYxgRzFW0LlAuSon4CoSIfTDaR2rfsYqG1tZB5n5UwcHKcGNpjIcPNZ8CWFyjoYzJ2WwJ5FP7uAoEVWcyMhKr71fFaB0cLA01a4zYRmIKl8CMl4cPV8amjRxF8rQaZRqGHLPF8B4Kv3Z0FM/RycmwogBWpBcQAj192hUoxC8iWhdnoKJbHHfeiIgOc1THzwYDiPUogx5GOk/8g/CxYiW0dfXRM1WjYVn4vfdSFRf+v7dFuVevoyNefqnWIzLUojmNeCQyBYEoD8OIjF0XsD0eH29+F026KorLh+IVeVlEgMWGImRTe54pePWsY6Ii3phkysjjBLIzXZ2PqiGCZlSV6Ljq1AqPXQGMFQdL7/oq/ceMdvX9aM+DrbpyLg4P81TPf/XgxTqPhPpCbySCgUIURW7m3dzyuPNGRLTpGNOkUvRs7Xpb5G4jLKLD7Hkeouca2/jNgyLhkfaUdHmjiCkAMG2OqXLxTbeiZ7OMkxVMi/WeVRSF3StL3UQKG1iWKPIBoF1lfiyRlapIQ+RiOs2VEnL/P/mT8V5T7ZvtwDNlaRVcBwfD8NlnuYKHp6/mOsJnVI00ZYjYksLZbGk4st5NPc6FmovqnDEab6w9S8OCMdemVnwlDMosDw91ZGWxWK4XPufPTVYdleFQcL14sV31kr3+ULvJiajsJsOiV0Ao8/kmUvfkhJcIgUGr14PZ0bjzRsQwrIS+F4po856tCVu7yST32CaTWjqLHSIlkPE+1kP1IeYohbPNnrM5SQukrJwzbxRMJiujgnnb1Tp3f47tM56c6PP88mXsLTHhHaW6oiqECAeDv7HnfPyYc9D4NUReOZsvL5gzBVWNSlR+7+pqWf55dbU53xbUfnCw2QXWnlWAHiteNzAHHl+AnisZwLOqjHyPHP9emENleEdn0j87nNWf//lxgMn5nHfkfPy4XrXinRa7fkzOKf4IYA5YesI34KuCOfFsam56sIzfbufciLDgDs+QVbHqlecR4S2UBRUBa3Y07o2Id+Pqih9ebEqUMPVSLkfX2dkqnRaxkb59m3vePqIVhUUXCx0Vq/RD6Em5VUpTx1QzPXy4VPT+3w8OVuyd6Efz/DkXal/5ynJN2dxmjcbYeVbCPsIEVOYUaRwWLmbrrJRf1D1TCXcoZoYROToahk8/XVdiPU2Q8HseKGmJutheRQkiQu8W3JeRsvn5YxFmxtDKhkpJVPZFZKQhKheVE/p04vV13rm2erF9NZ9rI8JfPd1IM2NVpR7AncPujcgHux+ArT0OiNrTMhJxdaURt9miKKWvvjudxnlWbOhtaqeTcW9EDDGW4PJyGWazlRhnZ5uAoIrXtr+/boxU0lfZvVUDmehwK4MVefDoeTKvwo8oEgFBN7YUDIh6FgqHB+PfpxcnEKWYsq6s0Wdx9ZxtWzIJ3AIrT2a9NVAL38tnYSM3bN7A3XFyUqvLt3J2GHKKf6W44MH7+auW6oETJeJc6FkTG0WqVG5l4L+PPtq8B9aClVJ+9ln/+VEXMDn+vapza89MNr+Zk3F6yh00cOcox/vqSsucHnZcnFE4ez59+DfaEhPxA2Pi2bPNwxNNhr88RSiG+q4tv8OGVJGOWzIk7rwRESkVAMmiNYchqAwRe7BsmL+avlLVCBCgVQ4KvI/67Qigh3liFjwtc3o3opz+4eGKvXAY8vmLQGeMTEjNLxMgUEhMmKlKgUpKw35WvVsE3GPRCa+gVJ4fgt8aqtkaZyNK56q5bW1Zamv/20Yazs/5/c7P8z3Bnr+q6MAsvIs0Ms6GdSqiSoJKepI9L9Jh1e8oHF52YS39uVIRTP+bWWWOLXONgNLgeVHnTJ1BpC59hOuDD3SXbHX5889+87PJ6+HLvf11T0aVb0U/jE6DDBgWPbQVghGCNkMJjxx33oiIDLxqyGs6jYFwzBvJLHTsHWVRs9wxvheFSX2O/vFjDVT0eUdF+8uibxUF4AFUav4gFFR5Hvt9Nb+KrAoCrWoYDENfSkNFZJSRUpVB0R5lYWkoozFl5ZHyi+YWZwNVcFYxRbwfFUHPuDuq5xb7JsKkqHlgeBeAfm3pILvXroB92YW0jMc4eGIw2woie/4ssnh1tWlA2fn1nUVhCDO9B2MzOmcwqtXfQUr28uX6ecI7Z8Yca3xm3+drB4vhd/aJlaSEjGrfy4iJfO22YtCCF1Sl59zxuPNGBBPMs9kybNVz0JlAQn6+h3Xu5mYzZ++FYtaMTQGVWlunwobHFPFLVKx235+iN2UAZk0bqmW4JKUgmLCLPMxIaaiW39WURhQKr5a79URRVE+A1lZoeP98jJiqMiLlV5lbZRh5JdeDoLeGsf2digdujc8qzqcXyId58RiG99H915aWQpm+ecOjDPi73y8eH6JSc7NZzCMBWaPmikVNMHfX15ukVTblwpybCi7D9vQ4PtZ6nAGm8d1/eUk2KmscA0WPkOCTJ5ttSjOhOZ/35QwrwmYH484bEcPABV+vImQCCQLG986wYFtrQM7nOkRtL5U2s7+v9plXiEpYTybLechyt/7dh0F3rZ3NltTe6m+2rTIDmy4WOlLHzkek0FTIWb3vp5/WlX10TivljD1RlF55ooyWCphWKQFftsfux+bKspnOZusAWPV5lk5j6aysPJYZH9lQzxQ15rLKzhoeqksoiw6wNFRrMUnYJ59sOrFewcNAtzgndr8Mu4cIBHNGrLyJDEOmd7HnmTzJgKN2n6vfhUPlK6eYjEFH0A2si8rXZMrj4KA/p+VDwwrxzCa3N+zYMe6NiHeDCT4fVTg54d4kwwUoIYZQIQSiooX1+202W4UDgcD2ZYuVw8rCv2wvIx+Z7XP/7irciftVc9YMlBZ9V0VnlIJUXnH0vqzGvTcUHj1TtHcgFFmetyqDouevgGnBumqF7GRSw2tVjFFv4Ph3/cY3Nr1g6+CxyAczyOFd9kZjxqQhmK5QdNAA/dnIm+dJ8c3FWCuGHsOyipuwjot/lpOT2HGIIgL2/v49plN9HqdTfi+mLyPsRBUfwdK9P9ivPvS1t7fMGflN5x9URSugcKJa3wpWAhPly0x3PHZuRLTWfrq19k9aa7/WWjsOPvfnW2tDa+3Hsnu+DyNCDSbwPce+BYoNQw0P0HMh9MaAjZZPoRJFYZ6oEgDf+Y4+UOqwRu/94kV/KNc+b2aAsMiFpQXPQK0V1DY+573sMekBNiLOgp7omBe+DDtSiaRUfjOLvlSbPGUh6N79ooxCKCdlOKn1rDwTSLjg1X700eZnFB10lrKuRnhu67JnfrFYpfejSIw/l2x/wygaQyCXnU0MxTXRw0Ttrx9UY2XehzqgUY7FW4c2dORHBdX/+8WIaK1NWmv/rLX2B1tr+621f9Ra+8Pkc0ettf+5tfYPfq8bEX5kgncXh9ozK0LIVbx4n5v2DJKMw0QZESysB+udCdmolNEKFFQhoZ49UjBesUQkWVYAs7w45gDhZf9eUc7WXsqA2pZfQ+0dzBMr6ewRsGy9svLGivcd4UAi+eaVRiUEbeeEVU/1lA+y380iM1no//Bw1SNHfQYpO/bvld4Q2Rre9gVdVzEMZzNdcmzlyJgumtZxt8aNMgAZ9wVz5HvaoC8WxUVgD6vCmMqYJSfyAAAgAElEQVQoiWqGo/zdWBri4ti1EfHHW2uX5r9/sbX2i+Rzf6O19udaa//T7zcjgu0Xyw+w7aFGa2x2GCoHjVV4eC8cHgQEJTMWVJjcAjP9qBhQp6frz2YNHtUy2gr4CiYiew511iyoteJYeIOtmhLowUL4qyrgbApM/d6uIhEKeJqFrz2IthKCbm2VCmRKeoxBjwhANB92v0b4kMp1fLyqxkNqo1LVwUZ1r2ddPm3aNkuRPX48DF98UX9fX4XF3qHaE8WvjZVtVQPQ7zfF9ZGdtR+k8arhOlWL7v8ty/2pyELGaHlLY9dGxJ9vrf1t899/sbX2t9xn/uPW2q+8+/+/74wItV+ilrgQVChvOjqKqXlViLXCtBbtFxyWygFlz1YpM84iaxF3PqvOiABd9rLGTcUD9e9nIxlAqmcpKXRHzBRxhHGo7C17Wap0KB7VfpzV+Ue4HyXoPTYhmns7IqMIKcAoOtOTFlRAVRYVZmcIGAPVDI0ppywqwS7fIwbEdVFvCDaYEe6jjqpLKls/OBeV6AIDuNq/QVawvylsEtvDDx6s782PP9YkXhWDONpv7N+Vc48uyvZc/drJ2+FL+7AWGdsTtqwIAdZdbhi04Is8vx2MXRsRT4gR8TfNfz94Zzj8++/+WxoRrbW/0lr71dbar/7Ij/zIrU5C71BlgAp4ZEFcr1+vU9NG5D3YGxYVDCHoPQzf9MaPattg3JMdanhQmSGR/VaPgMS4vNS5V+sJw9jqTVH6qEJVMdiad3vGUUap6tizRm7q94FtsF5xZHz5+yJX74XgWJkWrWX0Xebhq7nI9i0LmUfvzM4vKgxYmitSTthv1Z4LLIXDsDhZisgbNSzqWI2yYx3UWvlIRYRduLhYGeHs776Kjf2mbdTl9zdKmi1l/DDUeXd6HXJfCPGNb6ya0KE9OtbiaweL4b95eT38t6eLJQ4kstpVuKSyaDaMZ+/TU5++w/Fe0xmtta+01v5Fa+3/eHf9dmvt/86iEb+XIhHDoHP/Hnjk90+1GZU9AErgecHq67m9p5IJYhvCRMTE/p112WTDH3omJHpTdMBQqGe3nhSeMev06cP98AjHhqjtBUxLhA/JlO/5OTcwexku8e/svWzpnhqZTPOgYrZ2yojyHr7nBOlZCwaqZcofQFv2TOA6sMbYyUmu4BeLccyQuFdE0sXWuPpZZswrvFW0zvv7y/NRiVTgnoqu3BoR6jefP685BZ6/Qa0307c9w8qWnrXdOBu7yh+ycJoNRalJuqWxayNi2lr75621P2CAlf9h8PkfejpjjIU6xjtbLHTJp2qGpcBLh4e6ptoq8KgFcnZ5ZkNVbcTCqtuGanvm2hrl/m+Rd2jD/dbL6Z0n/yyV+fbUwD3vXZUJEL64lEGTOSrbRCIwVDpH8Qq8fduHLbKpKAz1/YcPY+PSp4Eqcn8bHJSPgGWlwhnnAYavgsD/V1GLyjmrGnX7+/zseW4O9ZvYk3gHFYH0BrWdwyzVV5E/dp7GOhdrxm0FyYwX6bVYWMmoauaz43EbJZ5/trX2T99Vafy1d//211trH5PP/lCNiArYLfsuUzysqdH1teaEuLrabHhzdra0yNUh9Zt6DLd+dFmjRIVbrScZ9WWoCEhlzGUC+vXr/gNulXivx5tdL1/Gzxt1iPRzYAGnPY34PD/CZKIV5+FhLmeivV6NKtl7KA/f7hsmuFUvG2W0j1lXFmVgzajs33siWBHtuF9/diYyxas+4/cdk33ROs9meSlndrH9q9qOV+aU6chKOrOyZ+38VPic1HV+nmzKKOSEjVfJQ2/bGGeLcWfJpnrWM7qH2uysu6YKofq8XUalazuARox26mL0rpFgXiw2P1+5x6NHK2PKCkSlLFXpZPQ73/lOv+H0ySer+++6RG42i6uzFMkRi+J4b7G6J3ucmKiBWmWvKwXOUsEo60X0SO1ZRsxnvehIqduRAUKzfW8xFR5MNwybWKX9/SUYMJrrqAzRjsjBUZwHWYUYohUR0Hex0KmIsSmb1rixqvbqbLak586MFiWvszPtZdttcm9sOAwRYM4+AP6tWktrabOR734PqYxhGIY7a0SwjTa2PwkEJNv0Njz6ySf5Qcg28PHx+mdVpMAffp8HzXASFj1/cjKeFc8bU0xZ+jPiFVtW8VQFtbHDzeb74IATbVkcxcEBVxhHRzyqxNJMmBMFRM1K49iociPgyuQMlMrp6XoJbAbgzMjPGCEfW3+lcNHQK4rq9CgCD0zO0kkKqxTJexhPzDj0RnYUSWDK1ytGFa2oAH2vrzc/gz5A0RzCCVCVXX6tlLLPznOlZDRae8g2Zaix50JAAPNeIcaSeCHvLapwUBayqyxGLwBkxLizRsQ2OWflSauDC2+lIsQjK1rx/at3sWVvTBjf3OjDAOXXI4hhDCu+h4sLTgHM7mUBWFm1Rw/1M65PP13dX3m8ipwGOIOooRYLTTMvXgl1e1WjBfgdFYmYTFahWYZw94PxcoB1lEWV1DuqxmHK08z6WuyKcwMXYwZW4GkoQ2X0VaJAvhTTIvwjvWHTcJlDywxvVKmo847vZl0zVft5RB19Os2+a5ULJJq7CiFXVDqq0mX27LK/oQlnlSY8fEb1I4z7exv64/eQ0rizRsQw6MOi+Ovhlfs677GhLxb5iA5WpEwqUTL1PXYoIoGjLpBknZ/zw8sEbNRefLEYhs8+q3W5fflyRdxTyWHikFvwlJ8vHw5/8WJTgT19qmvX7WBK7fCwPse+U2q2puo+r17Fz2vnQylEeJR+LhgT6P4+59LIKmdURLCahhwTifDnnq0N8E5sf1dSfNVnUc/uIxJwaG2qCEaw10eKoKu1VapGzZs1OCu8Jzc3S0KqLE3fW1LdE6FXskjRXTNw+timjIxmfm0ogcBuhknExnjxor7R3gO48k4bEVmppvUQFEmNijKAByLadMpIVNY+A31lQKzKYEIhip4owWexHdXDxsKfaJDEwppK+UABVNHUEYmQeof5fPPsHhwslWTmHW2bZ0U+vTKUAmTARIYBUC3occHjZCkK9vnpdHWWqrLv5obv58vLOp9OFCFkl48AKydD7S9glbZt8/3w4VKpKwMTEQngVNj5ubnhRkTUNn4+X/4um1/b1tvOrWr5rppUMlCjwtuwZ+zVh+ws4Mz6eQO5lcclYf/14qcUsd4PHsy/cKWsCxakOgjsO/eRiNszInYBoFF50ONjLWwUu54FjVUooLOQbs9gkYzeubm62iz3jEiT4L16Twr/rb7nsQgs/O2Bp5Wyaju/TGCwKir7Lipt5D3GsXutGpnMiLmYUO85C4jaVB0pnJM3b2qRFxvV8Fw66vsqfFxlH1XzDMyOJUCy+wsRO89ZcHm5/N2x6z2fx4yTSB2qOT893XQCHj0ahj/zZ3a3/9Rej3RhtIcxp2rOxkTmGbgWrMFj3rdXJobP7F842yxjOtT9fuOJuK3rNnkiqqx40cUODTaPV87Hx9xrjUqDvdFRDeliqAiFimRASbx8qd/ZK3Kk7jygjlF17+0t58GnhSzTXjW86T0k9X5+HTISoWokwj+LV3ze2FOeXuWqlqb1KC7sm6qXZQG3LHURfbf6XGyeM7CdKrdXhiywSlnZalY5FEX+MjmfRadxLsZ0t/z5n99uDdj18CHff3YeVH8fxaiL70Am4l6vX6+/d3TO1bi5Gf+ueF+fkvDOSYbH2khZ+02jADZs46hckKfa7q0J33LceSNiGOpVND2XV0geS2ENgqiuWXFOVGlyVcQi+/dtIzTY7yo3m6HLq8KuJ1qXgQBns2WY00d7WOO9iiGgKJNZuaz3KNGlMpIh7P161s2mSLLvfvObm+h6j6eZTOISx+ja21vN86ef9pft9nqNSEuwMDrwERH4Ltpbfo6YjrDlz8PAo0fI0fcq/m1balfn2J4RaySrc+rD+z7141N2KgpUHefnu3nnCDdU0Rs/0OVM6DJhDqFvO7SpcLMXatYie0/j3ogY6l5Yz+H0SpEJquPjXCGxg6sUcwVcpnK6Ua5XXfv7K055/z0YNdW0gDeCzs5qCkl5R5WhDCavXH205vKSgwXZs7H39AQ7T5/y9bBMmgcHS0MUUSIGBB2Ts7XeX5QuYMZaj7GXXSBcy+jC/aXkq5oLFlGwxuJ0uryQplD7mu0jlVpUQEQr6xX+4uJCYxT8v0HZ3oYRwSjSlXyppDPU3rF/74m2+ue6vl7uqZ49FEWEtjlv+/vD8Os3ncIYh5/ly9jYdX67Y9wbEUPNg8N6Hx+vGrBUhdpYQqPI+My4FdTvRshk9u/RdXGhgYyZMFDlkxYZXWHIU7nwCJtg/015E0xgWc9oNlsaA1GKoxqJsDLDtyPe3189H/4XQhoGkDV41LOwuWTgUjSIY/vaK89dEXXNZuP6lrx+rdMJynBXTtpiMQzf/W7tTGYRj8hjf/x4Ob+TyToBGXt3Zlyq/YJ0YERxvs3Fztn1NY/mYU+xZ7fOhcIXKeejl2lyPh+GDz9cvwfDU9k9wZwDpL5YFLm6Z//+KXmhR4+WPw6lEm2IyILaxuLawbg3It6NSnrJg6lwyLF+YI70zHY9Hpv1OpnnB8AWK1tCeZL1VqvG78FBXyTCRz4ytLZKC/j57hGAKk/KjPKIWIYJM3iKGKp5mqpigOfWg8WwRk5PszZrsP3pP73590ePdLkdM2gY/0U10jXmmk6XwjsySCzfSjXdC3yILX1UQ823JRirRjxUed9iwcP9rBIK1V3smcDVwSLXak2+9a3t1ogpcIU5ePVKp2m3iUSM6fMyny8jEufnfI95/EtFTlv9jPOdfefvXYiFsVbNZBL3pFcWVEZResvj3ogww3uqltaWhemwQRUuxgqcjHURgvqLLzgLX1Y6hhp17FMYN6qtvcpH4lCoXB9KtxjALKJojiIDPcbLdKrBqbhn1fuPhBneFQDRXsyMDf9nWAwrlCB8e4C+iCio9wAGxRq7aI2tauVZuozNeY+xk81XNMcqpByNCBTp91+UxlG/i7Vie5edEbWuzGCISqwZgJe9NwwuRGxevVpxRWRpB/Y+LBKhAK9wpDLnwqdePvpohUc5OVm/f1bmnOne6Oz1GMSqv4pKxf3AAGfWOftwDxhHvZhatFsY90aEGZmwZ5spSgF45VDdpP6wRIpOGTiZ8I0OlCqLg3du30kBRtW8sqH4OiKFEt2rF4MRGWh4597mQ4eH696oVViq90Mv8Y59xsiDYjlypN38ex8c8EgX5tGvsVq7Bw/6K55scyr0ovBzFOHIsvNry+w9J4aaPxXxsN9X/AuQ4dm6IrJiI589jeXYebA4Fx8t9ZHVyn5jUb+s+gHrps5/FqGNIhVsVKL6yqjpSc2pZ7BzvhEB8yjk6Lq85Ex30VCdzG6ZaGoYhuHeiHg3fLi7QlmuUgNqDXsaAtmNqkLuh4dLIybrncGiWurQIM8P4egFuRdOak58aWVkZETeLOtYGp2N3kiE/d7pKTcWUI5aXTsrBG10x0aJfMqqYmRCUcE7wz2jvarKGO38HhysK+7MoMuM4+l0GL73vXGpjuPjdUPAKh+vuK1xNJ0u/61CHV3lQHn1ij8Le2dWYdPaMHz72/ne+c53lmfGN/SqAiTVeYj2FNYQv4lnzKJB9sxcXuZ6sdfgr76rMkzwPtWChspc4craCMjf6M37XVzUQG/Zw99HIt6fEaHyb9G6W779Z8/yA7RYaG+FfddWHYzJH2Z7qbqvLRjNhkmjzwOEBIxIJFSi53j4kAOdsnba3ii3dNVZO3J1FhWLKK4okpGR5ywWmkoZIE6EpFl1hnru+XyJ24nW9+HDpfGkqk0UINMqLc+Z41Np1gu2/86eZzLha9srhzPqaB8lAc+JxztZYzoyUB496kt5MY6BqtHA0qpMV0RKGhE2drZUBGkMfqDX4M+u+Vw3ssM+xFqw3jCR8o/eyRqU3YUQPdbS3p5uo4rQpg/BMYRra/eYCHu9jxJP5r2enMQhWXgMSkjYzaVIWKLD4sNw9rdADW3/rp5VlUFWcBpjGA2jy1O5Z4LOHlqvpPzhVe2lrbLOcupRm+XFgjsJ0aVYLltbCjukNlSvEdXHxQ9PgoNy0KqhyMoZHz3irItMaakyRlWSuljwTqmtrTeaquwTtW/V+VXrAcbVbN5UZCvrcunfccz5sXsmSvXgv6P3+OILDtBW+Bp7jnqIw6LzFskt/97WgPBzeXXF39XLSCh/BV4/PeW/f36u5zR7x9A7efp0kwxDKYvLy+XfPVBEYS2uroKH2t24NyIGndu7ueEc9JVrb299k2ZGhPVCgIlgQgGc+kdHmwehp1wR98uEAb57fZ3PA0s9sMuW5qnz5RH4UdMfzIv6vUpq0GIWMqXZm0uO2BZVOaU3kirej98vTPH2GEDeiLMVJn4/jSnJi85ET8Qq+r7qC8PWGM+aGSy2NLanQdMuCO2UQaz2hzKsW+NRJkQoGHYHhQOffVZ7VoajUM8dyZbpdPVMKmLHCOyw1lm0zj5jpAvU3ij1uGJWvhXctq89C1sDcKn6rDNLjFnjtzDujYiBRyIODlYbo8fDUJt0sYiVyenpeoSKCYXKQchY4PzIohEff7z8nCJuQbWG8nyVcLBdJD3Zz97eZpdJBZgEYdcYwYvh55pVtDCDrsJt0Ev8wxhK2bpHKZ3se6wvC+bJljN6zIYF0VYwHf4Z2Ryq/RGROlmuBXz+gw+WV2SARX1hfOqxkh5k+ykq+ZtOc8MT+BRFtMbwdco7BuFhBRR8dLSUFXhGW5lkMVDbAKD9OatiU6zR1suBEfFOqOdUmEaceWaslBim7YbxE8tyMxCuWYQCB7fycrcw7o2IIQ9RRcKuepiurmKF8r3vxd45QtvVSpAq+2lWogdLXlHITqc8L2kVUXTwrYJnStn+fUw6xRsqFcIYG4bPcqD2fSstyHsF7zBoAVhxNCoK1L83q7ipGrBINeFv2fyrcHYUPbPn5KOP1r/3wQdcoCsPmGFkYDApDz5KNWMfs1QNFLVa+2fPcjZUtT/8GVO/w+4LXIx3coBPqZw9ZvTYNCBTvoofg1UMbXOuXr2Km7ApDgwbHPCg3up+pSMCl9nwny/xUEYEwrbsBd9Dhca9EfFueHCkt/htCNtWLVSMiyxcZz8HxcuURuR1j9krFeGAUF2lnKsH9GeFBvBCWUi8CubC9fHH+hlsmmZsbbmdx16+C1zesKx6mj3CSylQP5fA2bD3rRqwLH2gmDt9lIMpdS/M7VB7cm9vqTRsV9nKvNi56XHsoCRfvlwnHmQtuv16f+tbqzYJUFJRySkLnfdwdSDS5/9dNeza388r1eAksXSjpW7330M5q/pORNA2m/HIbtaojTXMys5QRU5W5e+v3yyGfzNLBCKzIiFgmXUIq/nqiiPZb7mXxp03IhYLnuNj4WIWjboNmlkA3dhmV+2kvVCukPJUgJX2vqwU2X6OUcMOw8pIVqHcyNv1B/zyss6jUDEUGC7E/mZvrt+XmCnjUQk7JdBUmblNu1UHlN7FBfcOVSOoigHLvOJKrxQ818XF0gC4uclL5SsNlsA9keXm8W9ZGoMRO6k1tuWzBwe6OksR1qnLtx3vNVwzRcuekf3G4SGPRIFPJEtXeH4NGLG9jojfa1n6RtHGq1EB9VaM+bdvh+FPzK6H32jJzaK6dkwyyrawGVgYcH9/ve75lvARd9qIyDzbKFwceZ8A+SB8OQaJ/cf+2Oa/QZiDbp15btXyI6Y8IWAAFvZh/x4mRRuVQ+QOpXOREZSVYiqBEpUiRsaJV86+0VDFsMHnkAaw55t5iRE7Y9SNVc19ho3w97Eeb0U4w5nJDNjFgrePzyIRmL/ISGXv2tPq2f6eOiMR6ZknD4vOEK6joxUVvTJ+FW169V3GcC1AyVc/74GkHjsBxe9JllQEw+o3/zel8ypkj7h3NVppHcXI8WIywBqI1gli97DkfV9ti+H7bURuJvISoweMDt2Oxp01IqrWLZt3T4fNgHiZ9z3m8nS3OLzRXlL7Rgmfjz/erDiyQheHn4VqveBRGIeLC46Yt2XQUSSF5flVztUDVStoep9TzwwbBabb3+eRqsgQUxGwKJ1RjUSM9Vqn0/U9x1IPkUdu2REV/XFV8KPUbhiW88TC0+oCEFSdkcVCrw24fqzzcH4ee72e+rx37tV1cLA8Q2PvqyKdyri186OAhar/DEuZKWIu9bvDEGOyLBgY+7Pi7HjnPnK8/P49Pl6uQQSEHwZOMPjN9nb4fpsPv9EeD787m3NACSouImIbDIU6r4T/djDurBFRteB990LVsrcSfrMtZ8dEJzKSmZ7QO3tGFuZkXiQjkWLPyvLoR0eaS8V6NdU8v+38yZ4JBvnbt5v5deV5qrbX7LkyIV5pGe7X1MuMHmR5NFgVEoRwb4rIp/aqpGl+DqO+FeyyQLfeM6TAyfaMKHzB3t4meVb2+2dn6+/so16TyXaGxdOny2eupCWxFtbJYWtrgbVMf/VEPh4/XpWkZ+k99X2si4o62d4mttDh4CCvjML7MqNStQpg/TxYhO7gYBh+6Zf0b3+1LYY/Mbse/tWFyIdHTVv8YEKoEv7b0bizRkSPBQ/PVHkqFQIlW7qH3G9vzb4X9P53eyIRw7BZuswO+OHh5u9GBEr2cCmgYVaWCWHH+AjY81cU4AcfbHoKlfXMoiKKLA4X+GEwzz0phMyLZTn6aChBfHVVL2NmRqnyTiELo/3XYwjYUrsxynd/X2PWrGH0+vV2nA5oxui9U5RBIyWpUqH+HCowZGvLZ83SKtgrHl+Htu/WuPDGOTOaq5gKRE6RymQN36pnYBg2vfoHD+IqKzgQWEs8N/Tr27dcVlvWXTsvKp3bizGx8/MrZ2IzAxVeHSw8q9DKOx531ogYhnovC2zmquea5eAhWHq76O0i9O5HBhBlGJ8IPY4LykZ5PNXwtVKU24aHsR7q+VSI0hsVUV4e3fssYPDqqvbuni/CY0tYu/nMaWEGz3xe47vwc+P3m/q8qp+vrN+LF7w6YwwOwK7JJ5/o9CNSlMfH9ejM0dGKOtw2A6sYfj46oaoHvvgi3mOZQeaJn/x+YkaPOneZhw8iPFYokCnc6TSWXcAXXFzUorAqdWqxENk+hDG0y9S0nZPffB30oe9R/BACPiSTeWNbjjtrRPQooYz62YPxhqEvB1/ZaFEIsif03gMeam0pTH3/hYyF0T4XM7yy1tXRO2ZGT8+c2hC2VSBqreDZWCGrSreBND8+Xhe6e3ub3Abq8oRb7DntXquAaZURUVHKXqZF+9nTsvuhIjj7+8Pw6acxWJT97t6eJtFi18/+7EoZMdBeDzcB601TTUFVoghnZ9pYtekilSa0c6QMHGbYM9lyfa3xDNPpio2W7alHj3LHyTZg6xk9e9tH03x5/zacQNnFsGP/+Fx4p2xzZd5Cbzh6B+POGhHqkCsqWKyB4vSoKPOKB4VqjocPl/9rjUimkD1mQ40e8BB6goA5sueQ+HbRGZCtAoICSNMzJvayQforYlOslnUpwf3ypRZGY9D4Ue52bAorMpi8kchInNgcHR4ulXMms5RSfPOmJu96SLTGXL5HRWQ0P3my+XyRgZWVxNrLptZYMzUvm7L3QrVIBYcHDhcbDYrey6dFWAQzkyeZzox0aHVv20hED8eGOssVOfTFF7y/x3w+DP/kKuGOALtZRYj31qTvYNxZI0JhUVDKxlICtkQ3Egw9v+kvD8ayQ4HQkBdV0QeWs/aKxuZCoxx3dMHyZ2AkBdSK3gsXq1aKPlvJ8Wf8CpW1gnHjw7bTafy88zkXPPv7w/D8OQdVn59zwX962i8z2F7xAlhxGlTTdtlQkYgqHoa9h3+HFy/G7ePW1nsuZKXNLBJhn4etv1WK0b39fDIcg1oLduF8ViIRrXEyNMVZ4p/Zky5WDD2cKR+Vt+tpSRz9PsB6WTnEKBRgeI4BuKM65vIyZyLGnGEAAI75Blj3L8/fDv9vmw9fqgmtegv3kYj3Z0QMQ4wfYBZwdACqaYUIDPjw4Xoe3H5fsQziYvXV0W95Jkh7WDOqavub0fzBk7P3VXtZeQQK8KkuS0kcldmyFIl/Ni981Nn2iG1UPERCCIhuCGNwiyhvU4FU2fyMlRk2VaT2pzdOPK7o6dPxgHL2biovz5DzINDynU8Zd0V22ahLFpXyDKdebmRGtNr7QP5X3j8D+OJ+yuBCurQCKL24WDkbp6c8XWlLJ63Bk4G5LRizIn+8ofHkyWbKcRh0I7ZKCsw/J/AlFWDwmzerNfJl0ODkwX9/tS2GswfPNw0J5UVEpDJKMN/CuNNGxDDkKSaMSJBMp5sK0lvhXsGq6gzPPYHQfW8lR6WdscqPZngHVBgoghVV9x8pN8V0+MUX/eWHbH2z6JKKEKooiV2jnpSPxc9UO8RaUjo2r4z4ZpuhFHwlEmH3cPYcleoav6YKEGjPB5SLrYKohJyRQvSKu+pARHvJe8v+zFi8C0Lk6nnYyIi3WEdNm6bInBT/vvb8s/JGxoZqZQ7e3xuhvSnKTInjN1UquFJtMZ/XqNzZZblvKnP7Bx4tltwR/gF685ZVxbaDceeNiOrIBIkH5XnlgGY2w7Dp4Y4JqUWXMlwhKK2AG4N0Zzlvmw6p5IIr8xulMWazldfRW4kSRZf8uVTz8/JlTYj479h7Z+3hIejsnLEogQ0B70pmMMXs5zfbO5WICCIIai7t+6szmBm9k0l+xlDWpxR2RIj19Gk9ipw5F5UukUw/VFIuihyp10mxZ9CXwz54sPxvZhj6iqNqCia6MtKqrErMdie1RmnGvFkpc29tnZOm8vn5fBh+80xEEt5zhKE67o2IjlEJX83nGmy3t7dqtOP/vQdZXtmIynBlmIXeg+zpf61AingQMqVSzcs/eVJPk9jhhW8Fg6Q8iApIzF4MAFsxIrz31uuQVEeUIlD9ezIsSw+eK8pPAyd0fr7bMjsovOpcKmMHzKUWcqUAACAASURBVKiVvcTC995ojbiHkBrxKYIe7AfjolDXtuBlf9noStWBgYPmnwUpwOz8RHw1LDKEvQjq/7OzPu4O+xlrAEfPutHCXkUS3mOEoTrujYh3wwrpaI2uruKN8/jx0lOPPuM3kwqrVQ8McmtjDVcL1sowCDavinmrGiEvXuRnwOblmfX/5g3v/JedKcX5UFHIjBFQrZli5lOpFhax8tEV/+xPn/JSTxZpqcibaoko+060V6rGjU1RMKXVkyePzo//t8lE5/PZUNgF9MhQewnr8OYN/741yhcLvq+iXhNjwaPZhX4h4GYY+zsqWsAcKkQf0Xfo5cvVM3gD6sWLeP8h0qOMFR+VVWvM9nnVELMVYG/f8v3tIzRr4/eg0eDHvRExaPQuE6YZxSws314Mg83ZHxwMwze+sa5MkOO1jbcODlY19WMNVwaMi0COLKTNBIGqPmCgJzaYgp9M+LxWqhGUgK8YWspQssRAAMF5IKy/r18PFt72+XP22z5f7g0Bi6mJ3qtSuVOdD3sxnJC617ZKUClY/xkfxVCtqNkzR++MCB/D3cCrjZwEH9nrLTvchRHBUkIMj9Kbep3PlwYIiyB5vpn9/dWcWfkBr98zf0Z78PnzetrEGnvs/Rhrr9UX0X29XLq52Zxr75htALluuQvntuPOGxGZcOjxui05WBRiRP6VKRjfyfDJk829BEbTqkJWQ0VVbm7WW1pHpGcK0FWx0qvpjcphjSJIUdoiC9njPGddBFmZHzMYmEyIDL0K7iATqEohzOd55Q4bvWHoaG9W+z74azJZDwHbdfRVBhbF7+cE/8680uo7P3iw3v4aa1npPLmhQAauaG7jAngTxqsiM7P7U6WwIOtw7i21tFLO7B43N7lRNJstU8ZqPdhZjPY70g5RKmlsybuPCjIw9d7eqtrlf/vs7fClCrtVQnuZQLuFceeNiIjsxQtTJUgmE15adHMzDN/+Nt8LnkP/+lordeYpMg/K3rMSwmbN41pbdUqsRNJUJKLSpa+SM8/y7rNZ7nWrXHRm6HusR5bTHBsNiUZmuEYgWjXXVc9s7DOp+7F0S3SfCP9gO7T6Z7N8J4wvwKeKFNBxzDsD41CJJqD3g52XMd6+3YM9eIfWVt164SRUImV+Hl+/jqmlh6E2H9jLFdwLuoGqv6nIm0opXV3pNbaU4Aq7ZqN/UQUYw4yBOK/UJtzWsPtRQUPfwrjzRkS0uSuRiOl0GH75l3Vu7ytfWbVTtp6TD3PO5/pQsHszocpqmdnIQsg+PRIZE2xOVPkTK53KlGjkAc5mmgXOr5ufM+TZ1fd6FSWETc97VIGHFjPA9kZPJGKxWApqdq/MG2fPVPHQLM25VUbR2h4eDsMv/II28FmouILtyFJFzHu0CrWi4F++rBsCT5+unnlslURrq/4dFj9gFdrxcW7Y28hB5DUjIoHyULaOLM/vIx0MN1SJROB68CA+F0y2KLza6enmWUP1id0v6vu2NXuPoWyvH2vXw79qiTcQWc/shxQT2g7HnTYionlXQqhHePp7Yu3fV85T7Z+o3OjJk3VhDIu/QpfNwICswU9PhZJaI3y/opxZtISRUIHmF99hCm5vb3l/5u1FRlE1EpFhW3ze3abP7L8zrygzRnojoFbZQGmpe3sDEiHcLD0YedWetrw30hPtHWWQVFqXT6e7b9YEmYTW2mxf+pSnjcRUlZl1fpRBA1yW/S12b5bO8mknJg+qjRFbWypvZhQzAz1KMc9mm+kbFqlUFVUXF/zcZqk/S0z31bYYfrsVrEhm7SuhzhjidjzutBHBFpixRnomvIog8Rdq+RlNst9U9r9BMxuF0qK9xvaPikQgBDkm1M2UH+vAWI1w2GEVpMdnqFSFfw4lmJkQRUkh+zuMQdYAzLdm9/OTMRdWqyTsvZTSYHNdFfTRiIwcpRwUBbltk95rKM9m6+dU8Weo/R+Vy2ZltJExhnPH5APr0Fm59vdXez4ybrO1ZWyoY5/Hz43lW4hkho9GWAwJ1qYnAoj9nsmAyn2zSCT2hv8tREQUyVj0uzZNujQiOnJRldCpn4hbGHfaiGDzbnN5PsWENTk50aFBZVygJr2CFZjNllUXV1erA8ZqlbMrimS9fcvTH5nl3BuCz/AGNlKRrZVSXmyN7OdYJALGiDrgZ2ebIFf7/lH+NJsLBlLt8aQzg8ALZswBE/CfflqXMWpN2b9bA1J5b5bN7/p6aaj3ePCW3TVjSFXeJSI2qNRQ/AWM80EBbq1SxX2/9a0a54IixrLpKL/2+/tx+etsNgyvXvXJDnVNp5syzJ6J58/1mal0Ia6CdvHemBMvAzxgtXJf3xiNdSH9/PPlmiM1N5vlXCMZiPnkZCmzaDoDKPwKAppN8L0RcbtGxDCsFhgHF2HDqFmMAiTi+7s4rL4cckx7Wtv4hQ2g2AGuUtwJ/oBkYe9KrjlSwMxgsJ5uRThY/JHCbVxe6r4KqizPe1Xq75m3Wwl7qsiG6m3hv2sVvUqheQBc75peXW3Ok9+7rCcDq0qoeovV/W97HEReMoCB1ghT+8U/szfGJ5PNfayqNObzYfjww81nRidf+++s1822HUwfPVoakZlsgQ5ToM3IwMHcqYoTv8erkQgLgq0afRnexK5x9hzPnsV8Nr5sF/IrogL/exekmyfCH4yIxG9K5inccgfPYRiGO29EDAM/5BHz4q4uGC8vX26fQ2W18l5ZZeFtfF6V3UGIZCWK2V6+vuYKGp6g92q9oEY9OX670qfDCl4I6sh7Y7Xhra0bJ+o9beMxtY+Oj9f3YDWyEeV11R7LUlQ2H6wGE9TV5mhW0WXgzSgffnCwBFv2pBKzDrAPH8bhebtfGD6CKSar4BYLbYxeXNRlTHSW7f7uIeSCARnNj03fsWe1vWAig15Fo9At1e9xNS8HB8uz49N2maHOUh7sXQBwPTlZjyaxz0et0WczHnFMcWHRB1hofD5ffW4MMGgH484bEeqQ96Ckp1NtgUcHuBf0pK69PS6Q5vNN7yXq1AkLmilmJoytsLUClnm91uNVGIXDQ166qgwO3I/l3JkBDm+gMtfzOW8sZPkomGBShFjs8gaCCo2PzRdjHioloJms2WaP2nB3hIFRv4HSxcmklg7c9vIcIuxceUIkNZ8R90BP+ubp05osQ9qgYmhVqKdhhJ6fc2VqjYBIh332Gb+/N6YxWLTt4cNNUKdPqSnl3JMm8ev8+ef87yiFj4we5mwpThv8/ddvxEFRHpOd6DHo9S3HnTciIp6IbS54Guowv369/hwZIpmFOK0wUIpZWcvKKleVFKwJjWL8U6BN7Onra/4ZRkOMkkD1rMhpqzPF1ruiUFk9vOejqLZOVp+xAliVD2Z52so+rJSAshAshscTPH6seTN8qXG0Fv7+LDR8dMS5Vvz8ji2NVHNmo2pszqOUpl03ZRh9/HF/6rPSzRNDgb8902lkuNk9r4wdz4/CdJj6jclkPfWXASEPDmJ21UhJjzWCkbJjf7OYtSjFqJwtO0qg6kgARP3ob3nceSMiyuONEUA4fLb0zgvV/f1NC7USbkaqAWFLKwwUePD6epzyQYWCJe7x92dNqLLudpFSe/CgHomIrow0KFpb220Vn1fYhmoTLqXgUD0TrX9vJIKxoWLfILe9v88rBSrCDd6rSgHattIVZ8je/+CAl4Jm67+/v+RqyQyJyj6ymIbqnGfrZlMNiKj03g/P36MXPFEUA9xamWIxFmrPR+/pz0xmiPlycha99+Bv/zyPH6/KPO3eU/cbY2yenGw6eT/xE6vzBD4JNVcZvTqTSdTwrgqK9zzuvBExDJxgZGzo9md+ZpO5crEYhu9+V697pOS9UhuGuuWO+48pSYXAYpwREaArU/owmBXuAofcpvqYIaYuNA2K1joSJAqHpIy0yrw+f65TMtH6TyZcqUdG0Hw+DN/73jIEe3W1Wj88O9JSilY5M1oUwVdrebtqPyoKGvTWY86iv6qOgVc+PdTcG90YzbuqNt/VCyDEqqNpqwIyA5GxVrIyZly4Z9QfxRrgqlw6iyxk+8NHhLyBlinr6Lv2OSFHz891pcvHH/N/Z/grG/lj+0viIX1NtBWUP6Rxb0S8Gzjk/3977x9j2ZaVh+3TdevHraruJPLDUhwYBiQsQcwfoBE2KMpgjXmDBk2PGNEz857wPNNt+zWkp614iKbA0byYVv+TEkrUJlLFz6B2LDWp2JGSeVGikuI4csoKlCdyQNAR1jAhDkmUOw4wkseBMObkj1OLu+6637fW2ufeWz39ai/p6PWre+85++y99trr57ckJwC5809P45gsg6NmHR8jSxRlsaOxIyAi7ZKX+0v1SXQos86ENoPZYh88eOAf0rKpow1tqwZmMz88pC8bKtL3qLWsZG6ZS1MUTiZsJY/CO3TZXLB+HE+eYD7c3V3O9q+1ejPhk8lkebweRgajTCgRldDVXGy/Hh7mchr6nocK9e91AzYW8x7jEbRjyvZkinLs2Of2/miODg4Gxdjr3WPxIFC5NPJaZvlP8mRq+Znxm+So3b/v34Pl0Mk90GfMKPUM1j/c+0hjFG1Gx1N68t0roKZEXBJyg9k18RiolGGjoI3JYIZrY+KIPPAWZklKg62ojTOKUTNEP9ZZT1oVW/e6VnpqmkBZ5Y4B6KD4MRJK4jnROAGIJ1CsX8JF+n2sZXTnzqJSiuB0+z5njXgZ+Lu7gwdi7AGVPWgyv8tSFrl1bDOq6XRQuOx8yVp6YTd7+KB9fXo63P/0dDl0MQZ4yHtXUVKQUq+VHQ1FzcKbbC+gShUkIxCsvV5/tK7M64D+po0UljuVbYoVjUu/pzzT67LpKSI3b85DQ1aeeB5E9PdHjwgz1YC1XBE1JaKPtXZNDM/j/JxbLBn3b99jj4UnnCPwFlY/Ld4DNFbbGRHNC8IGkGxz9Lyzs/mBiWLsLAM+cpPKf9FhgOLH7H0sToC8eySkrKfAy69BypOdgzGuXb1eDNefCU3dq4F5RZlyG/EyW69oriLrUuLiLMSBFNYxoclo7qUiyxodER97wEPTad//1b+Kx/POO9wyPzpatvRffx3fR7x02Xm5dWsOtS37AyVZ60RS5nW1uRc2eVnK1DUQ2Jj8EYQKG72vKAoo10fjNWXSEnQYRxt0T57k5nxvb8CM+APETEhIeNCrV+CZaEpEnwMr0WSteI32yLT/LEKjTeC5e3eREfW/vRBJ33Oh5ikQtmkOqlBghwrKks+4UFH4KKtIZ+ZBkzxHLAXkTpxOcUna7u6ip0HjVTA+0nwgzZGQIBEwH51zEt1bNzmKLB15pvxbUB4lMezNNzno1OmpL/S8WD0zkDyvkPcsrZTeu7f42YMHy3tEK23iAkehmPv3ff6L8nIiz53lWZYfsb297M2SVtUZxdbeC/Gw9Zp4OSeyP7WXw9vHzFKXXilMoTw9XU+FjeUBoQig7eZNDs/OKlBkLXTlGeL7DC6N9OQRRep7Dy7637HolSz+g2q4ZTNdgWeiKRF9nSdCvl+jENqQlVcnjA4YyeoWRtzdHRg+CpH0fa5Uk72zHW8mW1ssxexBuI7KJOamZIqaDgEhMCiUTR0JWW/95BIcDO87DBmR8ejZGfYMIaF6fj4PpXoeE0uzmS/gtTKmlWQvnMbmajIZnsVyFuz8oP4sfb+cNPjhD8/vi9bw9HSxP47lx2htRbnJypGaZGF9j5okTzR/CCHSa799crIcMkXlz5HFr5sa2n0+tmpCX48fcyU4i5vBQknMq6l7KlmvQ633a3d3eAfdR2OpLTjzRHgCIGLENVBTIi6pxhL24tfe5kKu7Kwliy4khNDBmRGGSJOWOKYcLpnx2fCFHQcTsmMVCPndj/94bt9kNrjkSGTWgOUtjBWGXoIicv2yZ+3tzdsT6996KJoyZ0jJ1W54QS6VezD5dXSE+UVKltlciSLhyUNvj2aF+OHhcrmreJdsZYOnfGtey8iRzPikKsV6LWsOKKREsD2BSn4F3Indg+1Zz8OBuo2OgfTX184O94TVdkxGV9QPxyKaRrzi4cbo//94edZ/pUz735veGkIbHngN6kCm/3+D8NdNiVCUOciYSxF5HKzbEHkOavDa0SVth7e3eVWCJRsykeQ//Y5WAEmpacYT4c0fKjsbmxNkK0/shfYNUoSkAkAsLesm9y4mlAWXgQmLDACVvafG7Ijc2lrQZ1E6RcBpLw0r28yUDXvJb8L3tU23orlna2yvmzeHGDXzdiCZ7M2h7lMTyREU9rRX1y3ypFXws54yaTXtdWtluVxyONq/s1Ch5VfPw6H5Df39xg0/dGr5ABlnLNRZcyGZGsnpKCyXCdvJ9UqZ9e/fv+i/YW82XzvtWhzjMl0zNSWikpiA0j0VNGUUA32giuutVrBqd6FHmdDN22/jZ5yeLivCVghHJakIAMeOx+s+WjOvNZ6IDGgMur8332dnPC7N9r8G+bJKaNbSsZY+4qUa6y9b6WIvSaZjck74fqwlyjprZkGSWK6H51lhxkCNjGaHtnfZkmemxNn96HkGhZ4+xc9kSY0ylsjgyngBWAmuyBFWWi3XZDKsC/LyP3myWk8iZpRFvH/rFu5mKnMne9MzBNC8LPBYjSZZStyNcQVqSoShyIpAh5B36NWEKCTpS6zAu3fnbsFslnIkzKK8hGfP+LOePFmco2wimTd3DPWRKWXZeZXNiigqlYywC3Z2lpsAIWKHhQgnm+Sp4ca1uxcpfR4UuJdzMOYa23FTvFKR10IAsGqBmDSvW+WUtQeX/frsGW8KxWLjst6oZJslUDK8iDFrIzxiK52iJGFPlnkYKOx6/fVFtEYWQs28494ehhAXb8fFBeedGzfma44+z/ZZQet9cLCcZJ59NwkJsnwgIabETiZDozmKoTFmczdPxNUoEVm3urbGNdIbolWE+XQ6Lz/MbogI9CfKS/DGipAzo42iCR38Epeu5XlvrN4Y5LdnZxhDIEqq3N0dKjcyfMIOKY2oGeWrIKVGdwplwHWRklWLvYCUOrsPPK+Ul0go0MXMsraHjH3X2QyHH05P594DnViskzLReH78x/HB5vWbsPy6Kl5EtMe1y14nP+tKFIRHwsZnQcrY9T3fg/9+dLQYzmWAaIgP0VxrZZiFPGo8WEzRkNJ0pHB6ISDN+5PJMBb7fRs2ts4AT4l1vV1jUMtaTsTVIFZmD0Q5hFBHOWR9eG5l76qpEtBjjhROlJfQ98O42cb/4AcX390ie2ZQWJnwzXbhZO9hD0TPc2eFJ2oWhWrF5WKgOci9m1EiNKEyNMQD4vmyB4jNa1mXJ2JBgIE1zXilvPFMp/j3Nj/j6GheYaL3JZvn/f25NyfrEZhMuCfOej60chIpCUzJsPlxkt+U8TzKPS1P3727mI+ClC40vvPz4fAfC80tHqBVEyVl7WVe2P1Q4iZrCvfZz3KPZ6Z8F3nizs7mBoXNIcqcJ9mw1hKUOrp5Df73munaKxGeEJSFR/W/rBbasz5qsfOj2mJ0RZ3+dNKfuH61cPEwICykteBj1IBkWeGZAVryqObZ0cEqmflerfuHP4yFjJRk7+3NMReYhexVP6B72wx2i0/ByFNeUfKgd7H8A219egcnM55kf2XDI2h/MSViVX6onQOhLO4MmsMaGcHKSqN5iMYneVnrVELXfaG+NdMpz+dCZc2iOEWGmsXP8c4Ab441vwufRHOssWDg5hY3oHXXSIzwClqCX2slIrJKLWPUCh0kvOzae7+fTOrczh/5SJzUiMavK0RqS6Lkt/a+GmLXkmwynVHtAS155AF8oe96XkBt4aN5yoaU5HrwYDlWL9DoEdKhrD/7PKtkycGEfv/8OQb5QW3nkRVuGzfVWuc7O4uWmY7xI1Aob1+OaaqmnyntzaOs+uycj10vxqNMwWTGjzcP3vj0ASllxDU8z+bNS0oV5bDmWaJcW367uMAGCSq/z1Z/lOLnnWTnGPFtdJ7s7CzCqi8x2sUFLnHKZNSuia6tEoEWUGJbjDFqQ1FMeGnvxxhtn/1G3LdjatNthUhWeREmR59FeQno8LeAP2zuorg2C0N5c6DzSTxrA80B+0w8EqxKYTrljd0kNJW1bD1ieTyMpwULIgsmpL1KbP2s2xh5VGqqk7TAFih3NI9R2bEOC3mHSuTlY/NdoxR7IT+9J2XuagybKByD7mXB4yTsUhNm1YemNh70s70Qor2s91TLg6gVgF7rsZ6WbONAVkBhE9n1XNy7h5VZ8fpSRvNeesN0bZWIGoUgqzmi+PrY5MCIiWtjeNn3FYFVIyROT7Hg85Ao0XhEOO3vD+/38Y/j5kY6/og8EfrZliLlwOIisOZpconXkH0urkjPKmFKiNfldYyMkMNWz6FnWYmlq8MvER95yWjRe7B5unmTJ25qb9be3vJhK9/LzNWzZ/5asGx9b75ZzopHFiFSkqutDBCZJApUpHghWHCt9DFl1Rq0+r1QF99M6M2Og8377dvLLQYYdgnjH/T9jAcHNRrzviv8rPn//NxvBaDH5DUk1Gu+8EPmWmYJehuga6tEZA9wKxCj2HWt9RHhLpQy10xR4xp0gLH461jNWy6GgOfB/bIs9ZrxdB0/7GrL2uTZFxd9/9Zb+H3sBo8UR9TmWC45QMa0gPYsR5YsiN5THxjoXcT6QXwkSodXchqNXQjNg/b+sOodaTttnyFNsCIezXhtMvyIOuVGVAukZhXlmrVBeAmWV3X7bvEqROXELJ9E8xbK7dAgehH4FgsVMgMFyRaEn4K8i/J9VBWiL5R3UcqyPEZKnv47UjDQnEX8d3Bg+BhtmIODYeLHIviNoGurRPT9cgmOvfb3h2xly/xa+2fw1mMsFpaTMJ3yDHx2gFuXMsJ/uH17dcVCXMVZ9yg7GDOeD7ahxypvkasx+q5+J/T5jRu+y9mLOQsQF7IAPeh0PWb5jjzHK3N7551li4m1fM6Eu2oUWZ3RjlpRMx4VnIKIbzLgZbWKnudx8d7XU3BrFGtvbTxr1ruyhhA6n5jci0pdxaPBmpExj4HkWNg5YV6ozNxOJssyPSOPEe8gz4qAzFnlTzBLojVLeSJkcOtwXSbp2ioR2Q0buWdrrMHsZ+LOtG252X30YWzb6bLqB2HKVYSO3qTofTKxfPlN1CmSXdrln1XeovACuocXLxerEB2s1mqSnIQ7d7jVuL+/XD4sCkVGPtR6nQQaWX4jFhNr+ZzJ5WHz6MWsZ7NlpWpri4eTsiG3N9/E7uNV5szK7GyVxs2bPN8tq8js7sbtuGsrwezvPZll7yshvYy3kXkRUCmnhC7Qugjcf/ROW1u5MJzmbfvuVh4j5T7DO6iIQuYv4uUwJ8Jml66aRFVB11aJqLU8ahS5jMUYeZv0Rs54pp4/H7wmiBmZq3B/fzWhY3kz4z733KORe5ElJtYq2JnyK0RSaYGEA2tlrN2pMicM3Ea/EwO/ybjrx4ZPtFA7PR14yipGkwm2DlHIjc09Q+JD497fx3whyaGZ7o86DIGsQL2+Y7pJbm3VgUoJMNGY5lp6baK9VdPxM7uXMveU+3g5Fmjsb7+N8wdYi+7sJV7ZjOLLkoIjmc7C3GMvUaC8ROWlwXlaTfNEvDhPhBV0EWVqiNGzLRCJPnAifvDwAKJLCzGr1N6/H2vIyLLQXe1sC3OW4Y6sUPQsiTMuAbCQeyKLypt/7zc6mQy5TdGYNfhXtE5SXRP1xmBr4L1f7SUlqegzVnM/tp+CjD/T1EuPwXvPbBdWO3fMI8baiHv3e/YsV+Vk96A3B9rLKDkNTHFDXgOZG/R7L9dD5FGmDFN7NFD5MGu6xvK7IgMnKr0+Olrcf7bS5NatOcDXKonBmZBE9hIPihBreU9pbHnQCLq2SkTfz+c564qKFLmM8D46ii3hyCKybstVDgx0AHnZzhKj1kpB9N6ZToIXF9xtbRUGpHhb4Rd5b9Ae04e8/o3Nlr97Nz+/AgcczZHEf7PxW3298QbOgVm1gyG7nj7lJaNoT2Sy52v2YimD100sQwuAdnISV9XYvaTHywDCzs76/mMfy92vZg1F0ZS5yjZnzChuUUJujdc0i5OiK0dQeGpMeSjj55s3+/7x4/w82fmazfLtzpGMyqKyjrkE2TaCzw4tnw15IISutRLR93nrJ4MSmHUje2V1mUZEIgxqvQ+oHDFC4bMHqCQb6b8dHdWNA3nWZjPsqvca4fQ9T/LyLGUkUJjVVFO/Ltf+/vAu2mqMvAuSoGqFeg1iqeXRLG93Xd37icdGw/5mQnZHR8sHkeQI1Apf3aju+HjZ7cus8AwvSthKI7pmD1LPlc8u6Xaq58qiw25tLc9R1jvKrFjtXWMW9piDUfqsrBJWs4o84+fplIcS9XcEURaFnJhyYtfk3r2Yf2rB+mRt0d+lvJrtQSoA0SJvUJG49koEY3SUOa9DDtbCYpsRXWLBI+aVzYN+p3sBZJ4jJXDaCvEOV2uNiLuvxuuQuVjmPnKVslCel3OB/s6SB2XPMejkbPdUvbYoBBXVnLNySr0u4nb14NBZqCvCusi+34MHPiBU7eEj61Vz2KAQAQqTRfF7z8ub8aCgSw7Qmt8g3tjbm3s/5DDxXOnsrGBnjP47grjWeSo1+12PKaPE7u/jqiAPsEzLtDt36j1ueozMAyq9O6J73b27OD6vXJVdh4e8qoS1aX/6lDCZfrkrKvO89koEYvTd3cFFxlpF6/pqWw0hWfce7oMITvRsVpssjCUHS0boHhwMB5oWLiwumLF4swJfrPDsQdf3fDN73SPRISYdIWsFStR/IXs9esQTyjTQk/0dK9mzh4QcLKxL4lItufrtKglqW1uDxZ+xtNgcoEsUU+s1QIrCzs6QfMf2pT142EEu1Q0sjGcp+y425JlJ1JRQELq/5X0W5mZhOHbGZMIlwnvMEp5O5w230LNteEr+bQ2FnZ3Ftd7e9rsiy3tJiX20Jp6C5PHI0VG+UiabjySeWwRKqD3Leh5dT4RX2SUcXgAAIABJREFUhREpGGuka61EWEaXEhzvAMxcOkbM3OFSsoMEg2dBiecAWS6spTbzcNVCv0qSU5RcJR6T+/fxPN65s7wW6HCaTHDYwxuzuM1r3kn2XBa7/+5dPAbPCtefWe8CC3dYj402LBhqqZUT2pU9m9W3ANfX1lbOayFWdPRdqQ6yh63sjePjeUKj8DFzP5eyKIC9ec5a6x7PCTqm1+MoE1IRRFZW9YMUIxvTR2E4FlJhfCPGi30X5InY25uHGFHoB82XeHGtvENjiTA4sl4eMaKis1TGpPtjZJNIdbhV85zl5+Pj+T5kyiBTZG2b9ldfdSZCJvoKyzyvrRLB5n9dyWhau2SCxB4smXiu8AFKmPL6M6xiYen7ZA4H/X0mHK1gZGAzyGOBxiwHyMlJXamq9f55OSniCZIxM8Cxvse5JIgHZd2jbqSIX6W/hf5/fUjahKx79/y1q82NYFdW2RRlA+1DyRva31+u6om8IbbbpxbgGTmA9kut4M/uL0meY4aDeKjYgeq1m68JqUgztAx+RqQsZ9rCX1zEXs1V5Zb8Hq0dkrljc5F0szKLz3N2Nq8o07KA8Q0al8uf8nIWFrMGfnRFurZKBGLEg4NlF3ltfEsu0Wq97yDXsxDDJLAHy9nZ3CKS+KZ9rtcILCtkhPnZBmblWW++if9ucQ1QaIK55pFl5OH/lzKgc6L3srF0mVP7PrYEV3+fVYZEZa3ye1H+5IAXOaAPDvReh4dzQaV5YG+v7x8+5HyJ5nkMRohc1ruRCXuJtyF7INj+F6KkZfcng6yuMdhqc9SinICtrcWKHE/pYv0/PCVC86KgwrL97jUpYwpULQ6EVU6i0k1vHZAyzJrG2bVjnqcaeRhd8r5RQzBNyPBI8SezQMZA+Y6ga6tEMA0PHR6RMoDAcIQZMozmjVHi6IgPsgAn7DnPni1bsg8f4gNdaq3ZIf6pT+HnIkhbJFCQMGEHtxVq2vr2lAy7HhoIKnpGxvL0+ApZHCyuu7WFM+nRWtcmu9ocHTnwnzzJ/V4uQdk7OuKWFhuTbgFeM3Y5GHU4bgxIWjROmRO0xtl6fTkQvLFpkKqTk9hzI+9v+QKVpKIQiBe+ZKBx9h4ZL8XZmX9+6UNcLHik3FqDSSe6ork6Pl7+HqraYfuzxjMbKbCiTLHKDzvXrI8PS6j90nP1olFuRKvO2HxOBMIK8JqroMW28dFMBUW2tXB2A8tlLUNdVxwJlJ0dngwqz7caM3tXeT8P90S7Ea1gkDgt8xZo61vfl7kvaw4LNO+eBZPZz5rvooNPlDZNzKqprW5A1hpL4GLX1tZiMqgo2xngJDQfmTCiHE5WYbHKcPZC7m7rltauZ1vit1Sv76xTdAmAWvT+iFBeAiM2NgktiWLr8bh9Nps7BF7Fwsinp1zxsO/36BFPrtV71XYTZfghY7A9ouoN2ZfeOCXnh/G+KBtWnp0/MILoCkMXiK61EtH3vtYtaxMxlgV/koPJa/DlWcEZqtGarbAUC6Am/0M0a9tK+ugIH2LS08KbZ3son5zwmm+rkHiIoNHz2GER8Qnap7YsNiqjrSkDtjKAgd3U4izs7GDlqQZEK+I1oSjXQ+b27bf9+0p1CHoem9MIu8Ra38irIfkV7F7IYzQmryrTOyHyWmYMTlYFdecOnkPE4yiBFFndmu+98JG8P8tVQJ4WD2KeeTYZT2h+tAf2W29xeYTkSWS4yG8R5gSaE9sJ9UvPA0FkB5DCzV6Nrr0Swag2XwDF2jzrKBPKqHWbe8JyVWRLT+nQ8Xz2fkg4MM8A096jAzjb8hkpKjrZE809En6iSEX7WZcEe3FpfUnlgh07y8TPeDessEV0fDzv+CnCuiZcgNziej7EkrTYJNGBLzgf9u9SKYDW5unTeaItcj0Lj4qsffKkvirr6dPF+WOHtIBFeVUJ3t7LhtMiYuE+tsaMx+3zUWKoeBJtsiHjf3RflvOBkEN1WKIG/M56lJgRiTyjNnxiZZx4diRH7uQk7/WDRk42dMFKnjZATYkghNZqOl2McwqDRTFgfSEkNktZjJBsg50xLm+BpxXBH4EuicUWxUDlMy8pi8UR0WERCSE0t0wZevSoLukK5b3Y/VxbRqvnE+VRIBhhsYafP19eJ1RxUaPA1vSz0Pe2yaXHxwO6pd4/Nff1QNjefpt7czWGAkq8y2A5eFdt7opN7osSHnVPFzmQMmGLaA/oveqhqe7sLCtgCOU2y+M3b877VNjPkBHAMF/29+fraSugPE9EVm6w/Z7tXWHliM7bYgBS+kLJyrPZ4In46i7QAp88iRONMr0bRlBTIggxS1mSuU5PF71EmfCCh8QWPRf9JrNZxIrxNjrrnnl+nu+UyNroevPI3pPF/r0D2SratXkkcg87n3rfobLaaK2YMhrN6fHx8npHruAMD0YGiZ236J5WqblzJ9/7oebyEpxFQdAHk9TmIys606MkcwixnIhsdY54QBCWgYxVFJ2oBNoLyzLZoS1oNg9RfpTwCPr9WCRJ6wnwfsNkak0H08PDZWh9z8iJPEEMRFDGyTwR4vl7+NAHq/uR6bP+K2Xa/9701rK2cffuoFAghvHKAVegpkQAQm5YvaGzlqq4grUry3ue/NdjXtvvQawTttlOT+fPqXF5C9PXhnQsed43D0uBfZYRqEyIZw5Z5PaWpmnIZekljTK+mE55J0ORA4xPmBs8UrKidWLz5hk1maTjdV3b233/4Q+vfh9t7TK3dxRu2NkZFCWPMmEHLUvkALENzSLF98kTnLOQ9WbasWTkgg23n5/z72bWRMDpnj3zIdWj9dTE8GxY8iryZjB57uWGMKwe4WExPu7cWfzs2799Lu8QcOB0ujifr5RZ//r2af8HNcz/sngiSinfX0r5tVLKF0opR+Dzv1xKeV5K+eVSyt8tpXxjdM9NKxHIzYgyjCMvAeq2pjcFUiTQ8xjzyt/FktUxs6Mj3n3QvqsuG2VlaJLUw2LEt2/7aH36eWjONKgLU7CYIGYuTgYlXkq+FJIdHkjIMMXCUrZaZHvbP5xQToQVplFlAKv88tzwrKS2Jrk3ug4PB36KEDVre5kgvo68vsiFr3/vtczOEvIiIqs6mmOm4EU5SojOzvyyxYOD4TuoNBxBOXsw73ZO9/bixN7dXe7m1yT8KnMjstP2ovHyZPR9WB6L/W5NCEWUhQ98gGNe2IoUywdv7j2tUyKy5YCVtFYlopSyVUr59VLKN5dSdkopv1RK+TbznT9dStm//PePllJOo/tuUonQ1hdquqUZJcppQTE0Jpj7Pj5ga5Kw9O/kEJWN5CG0MetVoF+ZNl9TgjwmDOARS7Z6+NC3AgRyln1nayuGzJ5OMS5CREjpyEAya/IOFJm/iwu/VFCjQWrF9elTbP1JlciY8FD20m3Qa4Vx7aX3hPAmaiXOlAs7d2PzEpC7vaYxXe2VTTr2PEvi7arpjloTmqi9trZw+TcywrQxJTIAyTbW1RgZVGNKQ7OXJHFqJF77jM9sHeeVCFsut0ZatxLx3aWUM/X/P1FK+Qnn+99RSvkH0X03pURkFj9q1qKFNxLwSACIYM4k2mYTIuV3yBL33HA6JCJhF+kNIW5WJiBq57oGSyG615geEHJArOKtyMCKe8oVSjgUF2iUMOeFFiLUPVnHmtK3jOzJuMEPDuYKOuInu/aRRWyvMaiyes20a15blhnlYuxeYOto7+V5n2qubFIg6/UjPMZCQJKz4nkmI3f/mGtvb9EzxOSw7q46pmrOQ55cp0fOG5c2Or5hb9b//k6F5jKGUZO0biXih0opf0P9/58tpfyM8/2fKaX8u+Szv1hK+Xwp5fPvec97NvLyrBzLm3sWA6/pKaHrmTNocxktt4ah5bsogxh5JnT76VWsL++danh81Yx67aJH4RQPiwJd+/vzbqleTT1bS5vY6iXMydhE4Ts64u5cebe33hovuDNh1NkMw5uXMqyTJK0x5Q31Uqmx7ASoKIpF679lLXOtXGSr6yJiiYioYy16pvQTqV3HTNjw4gKj9mq0UAbHj3pvIKpVEjOXBr7z2gUwL6aARzHlp9ajLHw3xthBHmzLZ791BhgDIQXKzTZU3tn3fb9uJeIOUCL+GvnuD5dSfqGUshvdd5OeCC/j22MqJNiZgGQM/fw5bo2bifFpuFgtHLLeFYZvz5rnnJ4uwv3WCE37/dlsOPxsh8bsfVZ1HXouejvemoY8kZcio7TKJbFnpJDIgekl7EaeH3bt7S0qNVmMAm8viaITWYmatLIkreVZDFuUgU9/Gj//R380VtYjnmOhP20hsjwqO2due2fwbO+ZY/gfKcw14IcMDTIrD7LK9JhrOsUhSTmEWT4Vyh8TQnxrsVa0cWkTY3Vpri25fvXV+e92dwdl/Pw8YWSx+Pn5+byWOsroXxO9kHBGKeXPlFL+l1LKH808eJM5EchNlWnBq//ubWYWQ2exeUlesqQFmYwDtUpm72THxJQFpFxIko8IGg2elFEALFKmFhbiJs5S5iCWJNa33sKuS1TS5dFsxnMGosuGw7IWJGthzHJYoiZf2QOHJeVFqIWyzszyErdzZuxiMeoyauZp0MKVVQn89E/nlHVE9pAV3o/g7QUPYWdnec6QJ2Jvj3tGmPfz7Mznye1tPGeiRGf7NqFcHe2lyfAGeycd1otyLTJ7Rwwe773Q7/b3udzNNBST73pKNruPwI17fAbnVCZRAxeNzapdgdatRExKKV8spXyTSqz81813vuMy+fJbsg/edHWGRulDC+aVS0VWnvYQZOqyRaBEtfxI2xa3MHJJ6o0oYQtmnWWaAWV5NHOAZV3mFxc8ZivjuHt3UWFj8LLZFt0175GZm0xfBUk0RIlcCPtfHwyMmNIqbu5bt3jOAupIy9bcc1WLQu3NEbNy0dzrckNZr1dfXfzOjRv4oM2GM5jQH+PlkffMhDHXwZMMW+PmTZ6boN3mrI+GHVfUYC/7Tnbt7XV0NMy9LY+086i9tvLvLOYEA8mbTDCwFXsvhDbtle9HfEYpgwan3XUboE2UeH6olPKPLxWFv3L5t58qpdy+/Pd/W0r5v0sp//Pl9bnonldRnXF4OM++1hTF75FA0MIXrV02bwGBqETZ66IgsA0mMLSonE4Edm12vCeQs0IWubSFtPue/f7ggFvv4gmKOgVqfkCCUz7LxnMnEyxsojbWjx75gFtIZmSSr5nlKQBqTMhubeG5Q2vmHWyiBKGYu4TKWLmxVZx0uaFdr3fe6fvXX/fzZjIHXSYBeDbL5+foA5rBl9eSRuREz2PGhgdhLwiZLNypx5mtMsnSbDZgXyAeiqDvJ5PleZXfZOWQVvTYGJBhqNfDlr96mB+RVzhUIliCjb0iYJMV6FqDTUUJM30fCxJPiDBBxZKT7GU9IxlrWJhyTCIdwsnPXKt6Iuw99ObMdkT0NqPcy+vgx8Zq3425JdkVoRUirIAoZOFlikfEXONjMsyZB4lVbOzt8UZb4u1AewklErLQjoTevCoU5qJHa5RpY5+N5YuigEJyqx68iJdkrBa47bu+y99He3tDbB55vLRMYsnkrMqkJmdiDPQ9UjYzTbns+8nh7ZVTf+Yzy8qr9wzxcmSrfiJgqz+kbCMOgbXdAF1rJYLF1yUb2dMeZTMwZvPWrLa6oEabvnmTo55mnhPlG0wmy/DC2ZwI794iRLVlmQEfkg3HAJyscjJmLVniX2aOt7Z8gYoO9Uwil/bOZOPQ6Pn6b7XhGq8yQbvDdXLkmLyS6XTwLOi/PXhQr/hMp7x9PONbvU8RLgHL9md75+xsyNVBY6sNZ1j6vu9bvOerry7/nuWN1F42t8nbL1aJySRhjoG+Z0aQlG6zCiL0nNrE1el08IR6MkHGj5S9CBuIGVm/dXax3EvDG8AGciOutRLhJbppjduDNkbC16vJHhtbFzda5rcaOEvCNOgwtk2zxmR818Q/WTw/IyC86+2358+Rw51hLiBU0WhtmMUdJbbJpcvjUJzZHhAZj4h8Dx3eNVUzmmr6DVjhxw7lk5M6hdl+dzLBSIY1/CKwyjU4D145qn7HGiUCvZ9cXmKsVayRFyVb8cGaP3nKek05pt0rzJOYyS3QuWr6vRlPSegSzfneHpY9rDux3CvLu9Np/F0J51kelKRa2bueR1XzwvZ23/+x7Vn/uwVsmgyS1proWisRfZ+rZBCPRAQgZGGN0fcj68lruW011ij5UapMGGCVhi+WcWoL1xsL40v23l4YwLPAM5fOqtYxYhsKymRZ18R4swrhG2/E9esZnmIkc+6VGmYo6/IV3ooO5Wh+MnPHkgMlB0TPExPib7wxn6MMyJmHaorecVUwKNYXiYUp9J4RYsqBbVXOlA32voeHff/4cR5u/OhocfyZnD+P/6XKRSD+xTi6eXPu3bJevEwZtVZikDEwnc4B4G7cGO9F05fA2qPPtLLHjAikNL9SZv3vFpCli7rgNU/E5shLdLNuZEbIRY2ssyiZ9s4dLsS0+/jsLOfqF0UBab8oaVM2roZHzgoBVHNuDzfWaEjmEMW4p9N5zNzWWVtgJrT5JLHSS2TU61iTbe6BHGUuVtJreYr9LQoVZVrPWx6IlFMB10Jlr7bBlRdXPj3FPV/s+NG6SZhI9oL0TfG6TmZzXiKet4qHrIEoE/Lv7MGLKmu8hEk09hrsCeSNY+W5qLOtd2levrjIGSE2gbDGW2vL8WezmH9tiXf2eQ8frgbJvrPDDRmkyGbCnO8rF/1vl8BtkbFEVqCmRFySp/XX4Bh4gsqCRjGBIp3xPEWSgaYwQcPAUKJx21jdgwfL2ccsH6EULAS9luiRV8cLVyArJLPprUKV3Xu11RreGtXU1nvAQBEfjOFfe8nBwtzAkr/Dwg3T6bwU16u4kf3AurZaz4vlTStTM2ubrZySihadOyXvzOQIuzL9H9BllRkvVGfp+fNl8Dj0THYgszXRZYmZnD8xErTBVeORtHOAStcze0HzBfN+6ZCyyNGahnBeOSfam5qn5L923l8ps/4rJXAHjo1vJqkpEYZWyXzv+7paYI/JRShqgSeWvcQKM/fSIDYSk0deEs/VqwUOm5+ocZW38S1FfM8+z1Zy2EuyvmtyC8bmttQItuh5mURYubL9dzIC3OO9e/eWD3bxlOzsDNbcw4f5eXn0qO//5J/Ea5b1ACFvgwcKZMMTN24sdqx98ABn2HvYEXIwyRrK/0vSnx5PFhZaK2xawZYro5h6cfj9/RjzQ8rGd3eXQehE1ljeEVwShIskoItjlGPmwZWwbKbjsMg7Vh0S5S5kxsoUWcSXFqhPKy3ilf14edZ/pUz73ym3+q+Uaf/lk814HBg1JcJQVH415nDZ2xviirUWq3Sf0yEBz8Jh4Q3P2ojqwrW1t7eHDxBpsFS7mey8raIws0M9O679/bzgZXyi56IWMz9SrNDBhECg2BWBUWXmUXp1MMHJQKkknDTGFfzOO5zXswoU6i/ivT8Cgoq8K5qHmIfo+HjRskShzwcPMO/s7fX9Jz+5rMzo33oZ/YhswiZKakXvqcsVJeSCZANac634sEN4Z2cI68pBu709HJ42YbwG7v/8vE6+ZIzJWkNCe5y8sKRWLiOvtXh6Xymz/n3lov+mw9kmcaUgNSXCUCYcwZorobI9rwlL5qARd2nErIJEiRSYKEYt5ajWHfraa7lNIolO0ffGIIJGa+VZfwJ/nd3k8i4ZQRPBpYvXpyZRsdYTMZ3mrfqakBx6N0/Z1N+xfFCj6KA5+exn8WeSVJe5T9QHJ9tkq+9zHsXJBK/LdLocv88eQpJYKBgOGWvdU0zRs7e25koKm9uHD+f5J5mx6xwm3Ycl8/57e4MyIZUVcrjaklGWHKkvlncU7YOoBYX1KjA0TZT3EM2Dp7CXgr1xNV7zdVFTIgCxuHyNcuHlWMgGyQjBCPiklMHd6gn4jLbOvByZAwCFV7pu8Z4CG5uJ/1ph661R1DhIqiJYjHOMwInmWb5zcTHkrmSyuj3ETsSXYpFl7p3B8tAUeeNkHBqyn61BNuRiE2blvh6ugZTuyT5FpaCMr0TJ03y7tYWTifU+zyqFmdLxsdVI8u7RIe4dKOzZOzvz5njoM0G81aGZ7IW8YbUhSPTcTPLnGCVCxmcVFks2uReNxTMSmFdzMomVLJuztqHcSZeaEkHIupuYhcKavcjvWWLhkye52DPLKrfMphsVecKExQ1ZFjwaE3K7IRjf8/Plw+HGjcXNxIRZZD16oRe9obzkRxbqkLbeNQJYyvS0B4K5iWuEPXr32sQ9/YxM2MhTmO3+sPj+VgHPJH8eHw+/PzrCAtt6yOS6eXM5s5/1StHrxHqEyCV5HdaIWLWU087nWFyU6BLlKioL9jxKq5YzsuvoaFmu1j6rdh1swqfl4ZrQNNqr1qBB/VuiBnlM6Xz4kH8mhscV5E661JSIJCGGYl3ydAIO2qgetDETAlHpnYbzjSB1WQ8FtDklacrDwGAK1uPHeKynp/68sk3rJTQh9ER2b0F5RKA1W1txaIXd9+5d/HcL6pXq0OfwIQPtEh5AkMW3bvGkWvQMUYQYwBpqMKQ/R4oF4i9bQs3ufX6O+d96f9ZxKGuEWJ3siL67tVWXoW/51SpdqPqJIUN6CqqVHyxpj8kv9HcbfhX5V5vrpfOPvAN07GXX4/u+b5nvMyHUDK5IludYOESIJaZLqf3XQtiCUVMi+rwmZ8skPY1YGMZaUVtbsYWFEC+zzIrCEp72rA8J5lqUhLAajX13t+9/8ifx/Z48Wfy9h9PB4LAz3W6RELCVGDY5jDXwsVTjhmW18Bme04eqWPVonmw+hl0PCX9k+UJn2NuDRx8m0rQtehcPZdDeH4UGpSrJ+/0q4QF9oUqWz3yGf1/c6TWHqeYr69WRMlGB6Paem2kyVotboz1Ikg+AoLpLGf4+1kMjnlavM693SRVKrRKXlR8ZT0Qtz3m9dFiOHPOyat55kQrFtVciapP6PGvYLjzyNkhszFMKUEJUllmn03xvC8uAjJGlSiQzj/JO0ym3MPS9bFayfT6bR2vd14Q9rEtTDmm2pqgPShYZT+ZvzCbPAD+x3hkZTJKMVWU9QUzQRTFjNA6rJLB13t4eDmjx0LF3YGBTtZdVHCMFXiuJIuwZb8iekLWR+arFANnZycEsZ3AJMiWHFxdYlq3qRTg9rYdb13N5fr6eMBOSuZFHLsMbaMxMFjx75qNVMw9fbUL6uulaKxHZmJf9TVTqJQuPOs4JQ3hKQVYrRkIVXdnMfC8+KdUf3twgq8a6YjO9KvT7sQS0jHUvQoApG3YTIrchW5Ma4ZGt+NA0m+XW9skTfm/WZVGvqT4sM5UJ0XhQAhnLIbGtvMck62lrm82XLg2UyoOdnfnfP/jBRYh3e8BHCiPiDa1QCO8xtzSSJV5C6u7ucPhmQLG80J/lt1pv47qgoCNFeXeXH65eV8+ay+6FyCOnCYWkvIR6rwSTeYbGeEmuiq61EpGJeWlCNd3M6mDCYTodBMDpKRaYXkIUshiY9qov1EkSUeZg9MbHsAwePx4OO+vNiLwrkwn32iBrSiNZ6hr6vb3BNZwpr2NKBII/R8IDWeoetDWji4ucleclgUYJmGJJetU7ep6zzaZspQm779jEQpSjw+6jIY4taJpO4kQHvOQusVDG3l5sAVprHilTKMlaeteg5zIMAV2i6c1NzWGjx2+rcmrKlwXroXatZbwIwZcBU4mSKI3XRBZEz/DmjIU1hYS3BI/i+Ji/b9ar63lZa8+uTdK1ViI84YYyeZE77/HjQZCzmJUty9OW+dbWYh+J+/djBrMWQ2RtypU9xE5OxsHGsjkqhbu6M0qLWNrexprNcuWyehy1sUzmhtTr4eVJeK5+lEiYgQy+cYO7M2vKEUuZKxLRPGd4DSl4en08D1MGO+Xtt+PEXjsWawAgYCRkDHgHX3SwoLVmhgPKV0HJdlqZtWv16BGWXZlDCRFyl0e9f/T4JSyjlZDMb6UJ5eHhIkQ/Ky0WJeHwcPitrgiTsvInT3IKK/PeyHqjubOhw0hx9w56mx9T4xlqngjn2pQSgYSb9i5oKy06dB484C7B2WxQNNBBJ1aybQ+dHX82JplRInR+wmTCBajnDtUJWdHhop/JktLEmkBVIUK17ZjHWMHaWkcK5tlZfSmn9SLp/JWLCyyMtrbmIFosUbI2TisCkoWFNGUSSi3CK1K+xTMwJqZuhXkm5yKaD8/yz7xnlphyZzEvsl4EHbePKors4cQUWG/dMlDPXm8ctOYov0mHInVIgfUU+tSnfEOC9Wix94paFOj5l/mrUdaZkSq8wYwCtJaCgYP6CF0lXVslgm0S1oArI4iYVeId9vv748p3ag6KTGJfzf3QYaiZXzR/qxh4LbVPT3kpWzQntUqErfhgAkYOa2ul6/cUQZeJDUeHq/Ag82qIe/3sbIBAZvcfU6WQ7VZ7cRFXIdgQCOr0KfM2tiuizTOxlVPaKs8cfMzyrxlDllAoE2Fe2PeSgzTykLK9ovnX9mGYTBYPIcZDR0c5hczjJeQZsUoOU/IzIFvRJfs6Ahbzyvd1VVf2udprYhWF7DrqNRQ0ZG1ovQi6tkoEi08iBhUrLcp4f/p0+TnR4YzcqJnEJ7bJd3fnULE1baC9g0eHXfSmPzvDApEhyHnCLTpMvP4lWTc7GgdLgrNli2Ose++5LIlV8ifQs46O5taHd/8xY826QqP8AxTKs9+TXILsuP7SX8KfWe8ait9LTowNk0wmOcvfu5AS4XkjtfWI7ueV/zFvQzY2nnk3nTs1m/E9bPcK8gAcH8d8xBQmSbLNwprXXKzEG4V6mKcMKR/RNZng/A3Zdyh518q8CHK9Nry2Lrq2SgTaVIxptZUmVjP6HsJ2YMBApcxr7D0NFLn1mMAT8BcRnGK1eO5pbQF4DLq9Pc/ZyCRz2ou527KCW1sISJOXv3vucTm8GK6BN0811r14l15/nUPmep6IszNqZJ7GAAAgAElEQVTMM5EHQCc0WgwS6+WZTObIhKybJOMVi/kgcNFZpevOnVx5rFhujNdYZUqGpxiKYQ1vC0qp/q3Hm9E7I+WWKYVR4zw7L1n+PTqa/waVXqJyQw9fJks1CpwkBI+pDEFzUxu+y0K52+vNN7nC5/WrqfF6sLyNTdK1VSL6flkLZUoEivFZaNNXX8X3Rsy2szMoIrZDJ0rK9Cz6aPzaZceS7/RnXmmSvmdth8r9fZ6TEQk3fQBHAnM2Gw4Wb+zefCAPhyfIPUGs8QK85j0oJ2JMS3MJdTCF0IJN3bjR9z/wA/MENvmczYu1hE9O5j0WrJIUKc9ZfIEIyIgl7GYOTC+0lg2xCLQ7m/PptC73xrrKdS6Al+iXSZzM8u/2tg9axhQUdsBly8ujBlpoXs/O6rwVNQes7H2k0Ne0obd8z7qaeh67Wnk7nfb9l54HFsEa6VorEX3vM0spc1d+5AWwhxliCt0q2HoXkPucCVDk2s/2thftltUjP38+jG0MgIsk+KCETM9Vi+YKzUnGdTubccFyeMiTEZlCpZOWshaBQIVbgcCsZp3cNiYUsb29GGtFdfWZHh6MF1hDIbQHpFSS5ZnI9zL5B9kDwh5smTlEv5F9lJ1/mU/xgNnf1eIYyN5E85oJYUVnhs4B8qpOJO8AKSjIizeb8UPVVjWxMEZNuahWVrM8YgHzvPmyoTA7VzIPtfk8h4eDN8KG0cbkMHnXj+w967+6SyylDdC1VyKEkPUnLl/LQBGAC2MKKeVCjG/jWV6yIHPJZYXf1hbWbvU7sJCNd739NkcN9A5RjQqnwzDou8za0wKhxpI/OOj7T386tix0M7SnT8dZIlGnzufPh9bXtW5alhCM+CZ7zygmfXCwPM4aq1BjNbD3rTlYMhgezFq3CYcRH2SVMQmZZOddDmgkWx49wjwXtfu2B6Vubx3hNlgFRbxrWUjyUhb7CGXDsvLsu3cXw4FWLjA5i9ZH7z2LESLzLt4Ntl6iKMr3WYdeyUVjmDH2XdaRbyXXK2XWf6Uk3EdrpKZE9HwRGUpaBCU7lim0u40pEZ5LrqbkkwkN7RKvBYfZ3h66zrHPmKDPoMLZ39jDQQums7P6pkCZS+LFY9fX28usjwpaf7vG6EBHv1sHJLS+X2YOkDDVh350CKEW4ehCCWVeeCra++gSBTdrNUpVFLLmRXGW3hQZwK8smqHeJ7bbbg3fRtVEUpYqe++jH8Xrz6x2ZpAdHMyrQLxwYDb0pOeIGRhyn0hBfO21RXljFWcd+vbytOy6RZVidu/Z/xcAtn9j96L//e3p8qA2iELVlIi+zp1k3d8sDjmmBEjfH7nqtrbi7NtVau/tgXz7dv19vCvqR5BVmL1kUFYZso5Ll8qOyVtgGPgZYKlSBl5C1TCeu1vLESTkLX9llS/BVMnk0GQawvU9ViQEjtp7zu7ueBmZ3fuS11NzEKPseoua6uEFeF4Tr6suG+PRUV1CoF6n7DzJIayTmNl8MX5moTLEMyj5U3JuUC8Qr4x8zIXwPTQxMEBUBis84uVAaHh2PTfn54OH9AvvEGGywbKNpkT0OcFgyyVRLJuBENUcalrwSKywFkzEChqvJ4QwJio/QqVxYy+rDGdL0zxadyxRX0jY6Gz8MU2DdDWO9pw8fYq/j2Kxkg1vqz4ipTWq7++6fC8WPZ633/bve3KSR0xkZW6yzxgPs1BZhrJKgT7E2Nqz9er7PJCQHldUUYVyeSTGzhK6swaGHWOtF0PCs9Ee1RD1GgsjKxuQMo9CnH2/fqNInoXwPaJcOz0/mRCN7uui+8Bob+zBwaUnYgdoYM0TcTU5ESw+u709CEvp/4CS8Dy3vBaiAhASbT6hjEsWkf2eF+p49MiPxY5pt8uEsOdFqA3decmnq17MjS5u4THejskEv/P5Of6+VJLYXinMzTubDZZdNo+n9kJt0j1elhK/rBWO1lN7f549W/bOWZCkMeQl9iGslcz6C7S3fH9VXkfk5QgxF/rHPhavs7jk0TxpfoxyZrKeG3voe/Ol+YbdG4U+st6+Mdf5OZ4nScxEMurePaxUondiidpnZ8uejpYTQa5NKxFWMEcur4xLzHoONPN7IYfplFsqtdZM5rm63py5nceGSOxc2Hm+e5dbqBllqSY7e13XKgfywcFyuODwcLjfnTuLf5dup5HQRNaurhrQLu8aS3LVS9y1iGeZhw2tpwV0ms2Ghli6wdKqSoQoOeKt8SoRhKKKAi3kUbkrC21F48xWK3nhtq2tOXw6GzvzgGhlMMK/kLWNQn/Iy6AVFslFsV68+/eXn83QMpm3T/NZxNMW5VOu3d1FTB4UYtVyz0PK7Pvl/Kg7d7C8efQI5859vDzrf/dGwvW3Jrr2SsQmhaunAGpBamv40W/ROBlGvQgb5DqXzSn3knLAD394cQy2j8MqLX8ZqFYpyyBFMjeesqRdhZsKZ3gCL1MGuL+/bIEwq13wGaImbN6hgaz4yWS5vXENBgISdFmPlOBWZO4hikK2hHedVr3lNVbCqLP3Zc9F2AY6PwDJBrQ/9fOiPRHNhQUFQ7LDfkfve2+e5PmCWssOYVG6a1qp63mXio5sLgeTiZ4nYn8/ViKkKVj0bBSKOTwcvNgyrmgfozVlniVWRfdKmfVfPE1qpyvStVciNhlX9xK+dAybNVPSsTYvVqY3tYQfWHvyrGdBuw8ZqEtNkhLDDkB15Blrm2VHb/qSsVhLyQoYfUjIdzJj9Q5Eb26YMLFuadbW2l7ibtV/y5aSljLMBxKobA6Y69vOB9oHFsrYzpmXWxA9zyrd+v28pEF2CTQ4Q6plZZRsnFG+yekpPvx0fg8KN0XzpCszvEodT+lmYGHec9klMlTAz1BFh/X2aZ4cg0DJ9i/aI1nQPNZr5s03+dwyOYzaMGyCrr0SgRY0Y21lLTIE/ZrdHAJhzYQO2tTe/YTpMjgHukkS22A1eRIHB9wS1zXctVq6FhzSeVQEtU3YevhwfFjG9oWQdbQJbigj/OKCl74iYWMtb5vbYp/j5btoJaJGKFslaDqNyxvt+qJYLrtknBG4EQthoQOJWc+eYm4h7r35QpgvEcKmKDsXF8v3RvPFwmdeLxn7/mx9s0YqS9TM8hHaH16oyJMFHu+x5oma/1mfD2+dt7by++bwcC43mdEkeXUIzI55rbwcMlYefVV9NK69EtH3sVVpL2Slscta2n0/zvsxndZ3GWQbLSPYmUaduX7sx/Az2LxqNDlPS/e8MTYR8rXX5vezh3A2GfPGjZzA0+5u5AqvXTcJ8WTc3d5BZ/MJ2Px96EO842rmWbu7vPpD52d4SZh6/cUqZla5t37ag4YUTt2YjlUtycFTu093dwfLP0KX7HvuXkfhETS3kRLg8YVO+swQO6T0JXJF3l17SO0+ySovNUrv/j4uT7ayheXc2KTd7e1h3k9PcRmqd0nyNYN+1+X0wovMSBQFQ4d2kNfp7t3F30lO1VVQUyIuKRtn392ti8XbJj3yrFo3qHgRNoWBYBm3BlRHX3fvDu9YA54i8yqbwrPqa6oxkBeI1W2zMUXaPCq3tJ+NWQN0mKCDw0PtQ7kkiO/Qs1hsGSW8SYjMe5+ovPDsLM5qz8TXa9uhI17QikjNfpOKBHkP+a0csNoqZmByDO2V9ddhhN5/f583LRP+QAiXmXFqpUw3dVuVNL95ni3POBLZUuvl1CEbhjSM1stTZD1ZEykcN28OY3r4kOd9PH169Z08mxJhKFr4bGKdZgK0aRnyIiufsm5Bq/GvIzdge9vPMvZ+J+Wvms7PB69NFsBIH5JIoDF3pDcuG9+uOdSRAqiJ1ajPZuPAqKIr2+LZU34iZEzpL2L7xdhnovp2j19QXoG+MtbewUEcFpIGUjVw02yePa8Vg7+2YRM5WK2SyXJY0KEkFQc1h0RtAioL/Xj7pev8HI9V8DsQv3mNqp49G7rmevznhQQySufe3uCd0OBSb765bCjpfXpykpNZEo7N8qgAcm248CJFTYkA5AEJ6cM8Y9F62rgVxjbGzoCmNKaFlAzZpKHbt+usqIcPsdWZeUfdPlgoC+OsL7Hk0Nz0fb17WZSA588HJafWK6AtCqTQoPttb/NktlUvjZlg1yljpUaK4c2bwzzVus77frUyYDn415XgLAe2Vsxr1mN3l4OvnZ4uljh6XXbZQc5c1yz2LlY9Cm155GGKRHyR8frI2h0fc9d91C8mS7IHUZ5ORmm3JcfIyxkpndprkUlgtwafd+3t5SHeo71ZGzZalZoSAYi5MS2wDQMJkvI+5E7Pkq7eqGV2K6yst0N+L+5BieFZhYY1/bFCxB6uzMrKaNoawS4DxBLNgY0VovGje8pas3LTiwseqokSTu08yBii0I9u04x4dtVENTk4apFEbQXDzs7wjtF6S47CpnAsxPoURTJaF7EYp1NccXB4uFwFgrLpRRlmyZPIMp1MuMWKEv/Eyo/W3Qu3eXwhHtes54/xbkYBjSgqw408JjLvyFjzDDfmDWa8GlVgeNcnPzmOx+3etHP1n59sXqNoSoQh7YbMbAhrcb///fGmzYxhFbebZi7m7dBJgJbxsj0R7PtFmvdY3Ho973a+mfYuHpro3oKTYf8mAFxsHTKCi72LVe5OTgaB/eRJPO8IQdHyLlMyWE6NjmFHbnDET8x6jnoASJmk5R+Jf6+a/2MFLLNWMwqPXHZfs/eXHIHMPff3MS/JmrBQ0Z07vnciG9JA3xOvy6ph0lVBtTLvkKkeQV4YJPe04cY6vyIZbBXMmoqW6XRAREafbW/7Hgq7N/VcfaI8679Spv2/uLnZluBNiVCkmYp1S0RwsBKrRC7QMZq4V3pW44nIbtisxiyJWagKYVVUy6wgyo71rbdilDq9UbPCwsY7s+8g4E22wkK7qTOVQWx9PYAu/ZnF3bftlrX3xc4H8o6tirOiPVmi6JydDeuXnVcGV4/2gLXMo54ipfghi2fPuAKSLXFFSXVa1mQhm+37orAsy6sR97xA829vr6cTrlaaEW9a5cLy8dERxk2IAMj0haDRM7JEe7KstzWS81nZIAnQLNH28WO8vyT09ezZ/PzReUVXCX/dlIhLqjmcmUKXQdxbZSyiTUeVDzVKZ80hwHiwNmFxjCASYZPV7iWuze5n14g10UHCQocUMuWbHrKovb/11nQdPsSiNs2e61XeASWaMTf5bIYxEVZJYJTLVmbUJJiJxY9CFazMTb9bhv+3t3HyXOTul1yEiE8Z8JS2ajP7y/IE4huUbKwP7XU3qfLKU1GYIiuDpWulJJna/A/LQ1Z2RWijdj6RzEOKNtuPpfDKG9lvqPz0+XO8juItZbln7ysX/W+XNRxGCWpKxCUhYTKd+iVglrLuwwwhTVZnO1tL9vBwGOvR0fJBGGEcrKI8bSKWffs23qA1IQRJpLKbTPp1ZNdICwux4m0GOxPWma6VGQWOucv1IcOUV88aZc9HyXAM6VIUADQHuk3y3l7fv/EGvkdtHb6eg5OTHC4Dowz/Hh5iECiW+yMX65OgP7eHYM2hhN5XLGeWFClKhCQbr6tknAErPXnCO7Pad2JljvYdX3118W+2z0yU18P4tZZ/mGxF++rgwK+80eOyyfRsD3v890qZ9b9bgkY0a6KmRFwSUwBOT2N3miZxl0YIh+j5+jNmdd+5w59p47Wei1uTTYzTCWZ7e0MZU00/h1UvqYtHc4WUKxQz1ALAlsZlqxlkXaQ/AGtQpj1DLFGV3bs25nx4OMdn0EmDiHefP8f3l3Gfn2Or3wpPT3nTLvf79xfL3yxC5GyGu3SOqczQyYtsDvf3c4aXxb5AGAgIp4G5oGU8UoaHXPKlLCtrHs/YSqnt7eWYvU1IRofWzZsc/jnak2gNpOxRg4NJSESQZBF/oTVHypp9HssdsJ2Pazxz6MrIBU+WIwUJPcdWXKH7svd58oSP/y+Uk/4PooetiZoSoQgdLjXeBa+kKhuzjizc7IapbbWNchomk0Xo7awnYh2YFV4IAN3/9de58oYoc8jbHBkUBtHu41o0vprsdxGyP/iD88NJ1lQfILr0jVkqDx/6JbhWSWYK7dbWsltaA1B5c6rzKsZ4s4SXvXwBhtES8YNXBmhDPFYpYgqt3ctjMBR0zoj1SKL9jnhrjOeBueElVIGacqH11HuTyS1RRJjywQ5O2yeCreHZWS7EZOHivbwNxB/2LGD4Jqg8nvGk9VIw3v9j27P+/y3gJS2m/pqoKRGG0GGQKZMaE5eWroDMwkVNV+yGYa7sp0/r8jMyHgWkhDx7tiisdnbissrshSoRzs5wwpe4hr1GQjWUTbwa8xx9kCLhPLbq4/nzeYKcJFGi70Y5B/a9WNLsmGoO9jftzdnamuchSEjAQv6Kp8pDcUXYJzXrn1EK9Vru7eG51f0ULNLnusbD5MDR0aLsYjKl9kJdLWXdWWK4rl6YzTiMsw3V6s/ZwYk8pejwz+6t8/PF9fXyNvTftWKhzw3k4ULRBfvurHJE5urevcV7vv/9ff892xf9lwuBv2yeiKunDGDLbDZsEOayRJtKDgv0G41QF22YMZ6IrMvMXpmsaNbR74MfrOsCicbtxTK1oK4B5LHrqMFk0Dh2d/PQw2PmeTrFIbTokhjpKgmuCAXPKoki/HR/Cfs+e3uLwD6Z9ZjNhrwLfeDZgxYJ2KiipbZPxBjSsXgW0xeFK8OjkeXL2pVn9nu20kOvdZanonbW6H2QQmVDYPZdrRct0ycCeY28iyW8orwNljNjZZXu3aJzHiTcKvkzmeRxrbhIPtxHPzp8BiszhAk3QE2JcCgTypANway7nR1c+hldst6ZDcPCMGKV6lh9JqwiMU3EuPrdWQIROgD39+cHw/n5slYuza7QbzN9QyaTuvANm0OZF5YrgEq+MvfzykZl3rS1VYt4iSxDGXO22uH0dFmYoznXrnh2KLFyZzR/TDlE68fCZyJM0VgyPVBqiHkFvDLnvb1ciDFbseB1LY2U3Bo02dpKGasoZJAhmYLhvUNtn4goCZbxjT3QUcUNK9FFTe1sFdgYZN9SOLaIXB+/xIj4cjnsv7q9pkYmhJoS4VBUspmN5eomKgKkk3WVi4AVzZZtKhSP041jxKXGXJD6PiymKXzoxWF1vJ69F8uelgRGNMaolFLeka2VN2fZMsUshG9taEvnf8jaratkdjodDnR7P1tKipRTD5xK5pV5IlA4TbxvNobO5h7hsrA9KS3uGbaBbvAWrZ2nJLJDziYno+vNN+vlSVSxgPZvRsnV1u/YHCaErxJ5ETyZ6nlVa/KN0JqNgaFHOB9asdOhNaTYRmtV6xWqvV4ps/57ti/6Lz1ffwhDU1MiHIq05lqMBcHdzxxarAwqsq6zio2+n0WU88CurBBFqG4e0MrNm/y9ULMaQTWM3glZCJ4A0vHKjFJXSl6Zj5TPGittlSvqjKpB0liOAuMZHdtG33vrrZyiHFVmWGs0UtA85SvaO1HosiZ0iC6kYEfyJKpYWLX0fyzPIaUh40Xw1o+V2WvFk1VtjXm/ra2BT3d3ufIpIYYoydbmzSElQjocC2XA8LJdkNm1SuuFLDUlIqB11G/LpV3WUdLNzs6gdKBwwekp30he8zCP0SIXKhOW6KBG1qlcAqBi55XV+4uVHlnmqF2ybqGrD4WxHTaZ1WffPxMGy1pp+nrrrXmIKhrr9nbfv/PO8rjseFllkCd4rSBl8M737vnet2xHXK0ksIQ72auexckOXPG+oXnVQrjG64L49dYtnkzo8Y0Hnx0pRhGNKdFGHqIMzwsxPISsPK1pKcDeT+fKSE4bSnC3BpZ+X1aJ8fGPc4AofQ+v95LIRNbYDF2vvrroxbyqTp9NiUiQ5yIUBqptUS0d4CQTHQk/FucWBkdCqDZxMeuyk7p4FOezgtk7pOV5x8eLlRQXFzgf4uCg7z/1qfg95HCLQhTSmhmNK3J5Im+CPMOuRzY+bd2/nhAVz8JsxsM78m4a6wONiyUlTqd+6EjyIfR9WNy862IsC30vAfSy66MPX68JU1YZQfvXS2QV5dPL/7DzKHscPd+L5+sqFd07Ax0k60gaHeOJQPMYed/YnNu9oXkh8hBmvLJIOUQ5MrVKkCgNAkCXmTdbYYkwTiaT5SqW7PpMp5gXV1U0I2pKRAUxZUL+fn7e95/9bH1mvXdNJr5iYN2hiOE0eqJlWhRzRU1znj3D9eLIws4yvW7i5SXxZfMDJpPFuWCIfQxd7/zcFwjaIs6gJEbxaVQ6HJWhadcvyhJn48+63UUwet/J9JuQ6/R0/r7I+2Tj52iMgnzp8V0EY7y9vXzgZvu9iAWJ9peEZFgFi1UkvQOU8YXnpVuHlRklVGv+QmNmh7XMTSQfPA+fx2cMrl6/E+oXw0ISGcV/lZBjRlYyRTcLe37/Pv77BuAh/pCaEpGkTJlV368/rn1wMACsMAGpGYRZSu+8M7d8kCDPbGrWRtnGjce4R+V5NlN5Mhks0Kw7r5Q5eAsbs3b32fdA5Yxy6fwCL2SU3bDIWyPzcHbGD3IvCc1LwmPYIeg9o/nOfEeuJ0+W9weqg9deJPlM3o+FBrRXKPLAWZ6uwQzwmt/JQeklC2pFCSF2RgeLJEdn3mssCd+xOTk+9g9rO2ZpbW7zI9AzJGyASHtm7JhEuUSgT2ydrMLgAUYhYsaJd0l4AiklkeKiDdRMSDeqptoENSXikjzmYYoBq2e3jDEGZlYLbAS5jIQI80RsbWFhndXAWd8EtPnHKFEsNs7K4krhbcXFapzNuODVkLwappqNW7s/o/eTHA4vo3w2wwJB8BXQYYPWO6MQ6t+xZj76Qr1FEN9nD2CLacIsTFtDz8JOdh5q4ui1VVV6bN5eyVqUDCZb5xfUKuHrtDLZs6UfzxhsGT0fXp8Tr1ST5cLY/a29dLVVMJqfPCWC7V1PHkhCvXfPyJsynWKYc71nHj3K98JZJzUloo+zijMb27oWddyTbTZxP0ubaPv5jRvDZ9olZ+PPDx4sCudai0zIC9WwTcMA0GrLFCNrDln+gmzIDotozSysNvu+LQ2M7isteuW9ED95yYTn58PnLM/AuuWZQih8YMcQJd5qZUTQFZGwtn0StrZ83tSeh0w1zNYWtvhsGACtB6uh1wBZNQe1RRZEeyXjCs8oEbUKzro8EezZCN5ao4Vm59GrMhHl2Y7FCx1H3h/PE8GUjCxYXTYxW/c3qQXAY++AkqJlT2S8ypuga69EZGN0mY0ti4yYMRsPFqwE1NkQ5QdYl17k9UCZ1R5dXPAyI4sboQ+yvT2/Zl/eR1tzKK7MchCmU5y1nrVQrReFhQcyCVg1gt4rnZQkWzZvWcGg+QlZj5mSQb2mrPTx+fMB+0CShHd3hwoSGzqrdf/q9bf8n42xr8Ib9trbG8IykTDOWLGMxzVlMCc8F3lmLPZ7witaOdzZ4cosw51hFwuHIn5etVRU3wN132VIlDUH8MkJf/eu6/s//+fr+xfpd0NVGRlviu49sru73NV5E3TtlYhsVnFGILIMfy28sr0d0LgQChoSeJE3wpZVRcl/6B5S+oZyRSIBLV1BbXa9Fy9mlp7umoqannlzYRWEqJzXHqra2vesa89CGnN5CWWZw8OzpJiQs8l+YmEh3spgoezs+AeLHDyZlupo3VDs2uZR1AJ6oeTMWmLljZaipE8xHlBuVjZ/i1UYnZzECLF6TvReYBcLP9o5yIaG2LprEnmLDBCLSSPvwfhF7qfn0Xautfx85w42BFmZsVbi0DmjjRrv3Do5WRzLpqHfr70SUcO0wpQ1ULB6cTMatjeuTCmRdssdHPCkLI2rwMbDDr3jY75BM0l3KNEno8yxA9JrkMZCBzs7/mbWz0DZ8qIMeiWMlp/GJJ2iSyC+GWpihr/knWT9vJryWuVHyjSj32SsWHFDR6iFSMCjBD79+zFQyOtIUssoejW8ovmerZX9jqckyJxnni89W7yqNM/zZhX5mlLRzFyy+9Xgk/Q9z0+QaqZv/dY8D1l4+chAFT4WJc/Lw2Eh7U2GNa69EtH3+Zr+vud4BpGwrHVt2UoBpgyweLW2do6O8Jit5izCw8sT0I2u0D0zJYKohfYY159naWgPB7OYM5uKWe1e7wKWj1B7GLPQBlrzsfMnmd9eH4J1KT/6Qi2zGa/UNlazFjZTkJD3y8NmKWUR8lvP4boF9NiwWXT4i8XtybDsIavv5xkOzOiaThcxEdh7jz0APfmA5kk8iptGktWhqOjeBwcc94F54BjezqbKPJsScUnZhi4oPp/ZaF6/CBS3Rh3g7IFiWwxrBUJ/r6Z7pk5cY4lWHtNPp3GfC7sJJHFUuzwjF5wHEmTzPp49W9yIWbd0lD+ABJwILpaRna3JL2WOJKr/xjw9UV8GTRruOttVcowQFaGche69cSPXDdE7VFhuy+npojfDuo+F71mGu+Z/ebbnAVsHeeWN7KrB8GCX4K1oXpXsf5t0O6Ynhb5WaSSWmTuGE8GUFbRvWdXbqldG6dvZWV5/W9avzy12PjVPxAuuzrBkY07RJVDVlhFZnXMWuloYQ1tD6Le3bg2HTC2DI22XCVlRVGSDMqVFf8fbmJ6nIHOo2XWsyUcRytSE2xhnNimMuZMlFCC5HSghFykf2cSwqGsgEzYehoZ3L52wFylkk8lyGR/iN4v8Z9eMVdnImKQiyuYMSGIz412tfDKcjwx/1Xgv5Lse9LXlR90iuma99MWSpvXfMiGPrPGClPGxHh6mINi10WEE8fSifbupRlmHh0PC7hiP02zGlVi7V1tORP9icyIsM2vG29np+9u3cwlae3vLdb5ZtzRjpGwOg4e3wC4UchCFBd3HZosjZUZ7CCIXuVdFknWvr6p9Zy1wD0OCjYElzopVYZNO9fyz0lavL0Pf54Sh11+iNhRjrctonxweLleGsOeyZmhjwwA6PwjN7/7+nB89D5WHRCnzYJXMbI5EpspFA2OdnQ2eCUn8Q54DlikkVo4AABroSURBVLvCyrf1PGeSLz3wNjtuxPtjiO0t1HOIVVloAw311ajNi/PWywMTQ9fJiQ9Wp9enxmgaS9deifASeTKVB+ICyx78sklYeCODKsgOWHa4CtgIq1ZA/TNQeaOQlwikN1+knEVzxrLXmcs609ejlqIKD+2JQG5PLxsbzU+U7MoOExH6Xlgu0zVQ86h16dZiK5yf83dlz0YC7+7d/HdlzVioiwnymrBV5kBH40PzIDkFkRc0O4fCB7YsV0r9kGcLvbvn7dEWsA0VWEPprbfwOFG1BsolsgplJrnWQ3e092Zzur/f92+8MS9fRvcRQDTxBBwf9/2nP53fI/bdj47i8NDhIUcW3d3dXN6DR9deifCyXNGGt4JJFjWzwTN1vhmPAROgGatNQh5awAjk83TKkwLRs6Ja5ii2afMDMr050G89BS8jfCKK+jJEDZoiZawWgpytcRRKiTwR+hBArn70XCmtZTz74EFOAbGgXvp9xwjMrKUs97J8PJ3Ok+wkH6BGAUYKbGYepHvv2JCSNLZD781CFPfuYV5AymQmjKPvf3HBrXYGKCaXVrA01oNdD72XbAM6dkkpcm3CsO0fYudyNosVAYShc3g4z1OKkFo9ecR4Z5N07ZWIvl9MYNKd87IMdnw8MHXEuBZYhh2yNrtc7ptp7Ypip8irINaEDkNEZXFow2QOPeZWk88+85nhd6gSoaa8C62jl/yWUS5kjN6hIXgWyBMxncaHnRa4NZgl+j0zJY19j/uTiFBmioLFhrCAaZHie37uf+55vbxqKPQbxhNaOZaciEh5Y8Bxdg2yym9NqAXFsb1Q4vZ237/+uu+BQSEKds/XX1/eN0yh0yEUlD/hHYqPH48HI8t4FLzr4cO630nIJTqktScMIb4izy/bZ5ZX5X1ZTp4Np61qQGWoKRGXZA+bt96qS54UBLeHD7kmapvt9D1fZPm7xiGImMGLO2tLD2nLOzs+lCyzcq3b1MaqM7+LBEXNBpAY5/6+L9wzCZD6O7KZGdiXKElWKHkHpCX0e4TSKN/V4FdRkypNujpD81SkOE+nQzO3z352HqrQc8X4/ulTXiobKcXsEBJ+ZeuFBCmqzpB/o3ySTEgusvrtemUTJBHvo/URgLtM6AaFKNg90Vi89vNeGM4DN3v8eJwCoMd1djZeEbl3b77uUVvvGllk96dVCuSd2VxruW+NsNksNli1clwLuV1LTYno8y2Bs0zN4oybasmasZb1JmAY/ii3g4VY9IZi1v4qIRu5WAIdm4co4Wl/n79nFDbY2en7n/xJfN/bt4ffWS9SFBayZAWOhNDYPTwrrFYBiyw6q5Q9eLD4+/Nz/DsRiPawRYoAInYI6Uof1sBNKwxIEdeKh3WTZzxDKD9CEkT1+GV/aICv6EKYFKseuGO9I8iilguVIttnsdyI3V2c85K9pEw+CiEwg1CUfOGPjBFWS8KfrELPKoCR4ZbxkqM8n1p5kKVrr0RkssZrmZox5CYWUYclsmNjSH1nZ7ikc0yzG889//RpLhuZoUoyivAptECwY7ZWmlcqyICSxOOA1r7WI3F2tjxHyJPFyoHHCr1agW7fyYZLRNFgCgaL4VoPHVPMpUyaWeICPYyUuoynITocoyz5bLMmdCHF9tGjfGXAZDLMmQAWCVS9pTHlu3LduIHLcJHBxHhLxug9x8uZYmXPlk/Qd6zCx2TI6am/bxjfakWAyR10TniGW0bxQ3k+mzJir7USMUazF82ZueL1xl8HaIodrxWstUKJ9baYTOYuMxFWgmGBSsMiRcFTMN55Jz9mOWRYvFW7pFdVBm0CKuMNZtU8eTKvvEG/rTnYmbdIN4KazXi1TSZfAH1eO4dPny7f5/nzYZyydp6iLq5dBDZkQ2RRgmvtXvCUYzsW1k8FrbNOYETvjQ6z6dTvd5AN/9nnfO/3Lv7Neo+898heCICOGUynp7i80+O7g4N5qarMnSiDmV49sq5IQbB7hRlYGSUiU82H1t1io5ycDPvK4nxITsbJyaIiubOD85Wya7IqXWsloiZ58saNgYF1/wQB0fFyAqLDL0uIQWsEvgahQe9mwXfs9yRTOgMJGylSNcBXYkXZzGwb73v0aHxcVG9G22q3Zo5F+4/iqlpZY3zAlAidCBuV9Hr8gxKvslgE+kLKin1WxsoV64spYCcnqx92lq8yYS1vv6L51x4tNp/iPWHvn+lUit7HCzl4a8b4KOud0NDkkcHEPDde4yn0XpPJfK+iVvDM6Dk+Hu6F+lF4+y4Ku7F8KPs+0okZyVF9nrCQF1KiBWGUeUHWZcQyutZKBFv4119f/Nvt276wqYG/zST0ZcbJkvwmk+W/7+3NgVYyShNzhbHOkRGzWo9BLWx45kKCecy1u7u4Ntl8GdalkAkCi5poS9ai5Cnm8kRIn0zRs4pY1qqTa51W7XTqr6HFP1iHR2Jvb/AqjoWuZvOqlUSmEEUJyZqifSvJt6enuXmx3iM2TvQ3dKBrN3vk6Yo8N/ogFXnCQgwsmVnz8uHhwFdHRz6Sp34Hr5twzRoxD8vxMU+mH6skMyVnjMFaS9daieh7fgBq0J5al71N6KqJsSKqLTdlmz97SEjpYM04s8zKXNJ37tTld6Bra2tQog4PB0G3qlIh7+wdXHt7Q4b5ug41fYh5ENU2+cqzNhD/sDWOqgcODobqjOfP57kb2nLO5qXUXtrC92LgNRVV+p0iLyLjbz3/2mMma4HKceXeAi4UKTDscDk8XPTMZfldeyLkvRBWhJ3/6XTgSX3ITibLCjCjyHPD5j7yDrA9UNOeAOHbROij0Rqx/cRkaS2gG5oLNH+bpmuvRPT9OA1atH8GWCIJXVqgZHEAMs/3hCBDWdzezoVBUJwu2kgZpmXj0tazCI1VFICjo3qY70iwSJy/9uAVgZsNi2iLyBt/NizC+Id5m+7fj8colrTF52eJc55Cx2rmx8yL8C1TMMSVHD1DeFX2L1IO7PwinmXGhNzbe37kmj45WQSNY+/z6quLf9Peo2yehQAhRTgi4rljiKk1RpRV4FA4w3rutEJb6/G0HrxVQs62q2Y2wXGsJ2J7ezkMW+vtXoWaEpEkVOsri5TJlp5O86WFKC7Kkihlg1tm9yowmIteo7GhcUTWmNcPwHOZIiZnmPaZC0H/jrmP9USgjoCed0cUzaixExIwzCqxOSKRBYtq1UXxsTyQjanXdIUtZVBMkKtdeoUwXtU5SFF5myjRDBI4c3neRW/PeuOy+SneveX5Xsm0PlijA+foaPgdwgWpObDkfaPGgFYOonBXxnOG5MmzZ8vJhCjxVIcHa7yDAgvuYfZkFAr73doqPVsiLkmrkjiJ9t2NG3P0z+mUh5s2RU2JSJAwBkv8yrrMdCwcbSJk3cnnXikfsnZqXYCSKDqbYSHmJebZ+ZDEJf17JGRZDxB51tiwhi7bsnFW8dq88cby5kbJo1Hc2zvUrICUeT08HAQiUj49i1tyW1CbeAT+xBQ7mQsrqLKhCEniy65HJNwYHLccehYkCh1+r71Wr9ywuY8OS61siKL9/HmuBbPnsq5xf2dc38yzIods1nUuSa1j5vbtt+sOZbbfaksea3lBUHMZKJ4kdd+/Pw/lZTyvep/Jv7NeXYtrUgNUhvh1U9SUiIBW2XzsQiiEbJNOpz6eOuuZMJstW/KS0ayfaTcC8nh4JVyZsjtPCIzJRM82S0LeEA1jbL0KyIOC3i/qgYJKLLVXRECkbt5cxpxA7mbrHmX8J7/13MbeeJlHwF4ClV3L95I4aRXoiwt8CDCrfBXsBXZtbc3XP3o3Ubr1/treHkKY9rtWgDP+lpylbDOszD4RJZ0dshlPhDx7TOWOXvesS53lTaDGhJ7XTipGtOK6vd33P/ADmJ+Rt8BrrHjjxjxxEiVKZuVClmaz8R625onor1aJsNYFYoTa0spIsPT98P/oMN7Z4W59ccGxA0MOIfl9pAkzRkWNx2STZuZCBFGUhCbzwNz4Irw/8xn8HJ0IxRQrJExlra0gYDkcVkmJ8kfGuI71bzNhIbnOz/3GaF5eDvNe2Wtrazn3QNeqs8TWW7cGwWxj5oyHmVW+Cswxu8Sjx/hP3MU7OwO0PcPnQKWbLPynAd3k2V6HVkv6PiwUtbs7lFQjfrBlmSjEJeOPFLcopJs9yJgS56FiRkqzJLAyWcU8yTWKsgBJiUc3g0FSQ2OVONmrm6SmRCiy4YTJBAvsmmS5x4+XmdQ24ur7ce5Cr3JEyjGRF4Nt6IsL/k5WSEyneeQ8LQRFSWPClgmE01Ou2ImQ8Vzecvhkk2CjHA6E28HcmzVZ14eH8+qHLJ9a3hrbon02y+VECByzlzeD1mlraw5gZpUtFF5jeTvZrrm1lxzmSNE8Po7DlgcHebwENnfovbJVIyxhE13MW4e8XxkleDr1KzwshDeaD1HIPWTK6RRXTbBcixoFfl2X9FFiWBXs3b3PVkkUt1Vf66amRFzSmEM88koI1Cz6O7MsMkpMJPR0C90MxLMwKoMmlntqV3RNKd/29uKmRpby/v5yiZVYWHfuzA+fsZDVolhlNuLu7qC0sBwO7yBmvDVGAKDENCFvreyYPYFr+0V4Coq+MtaNPIftKwlz6QNRDlbP26BDePIOVqEdU+ppPXhaocnIBlaN4c2N1x3Ulp3acBxSUqLw4v5+fKjY8WeUYLGyz8/9XB9vLjxLe39/jlopYFIRsB+TNVd1MYC+DB+gz8TTN6acfJMhjaZEXJIXTmDY7tYlqBsm7e3N3Wj2d6w2uu/jcEok9JAGzASxCCU5oD3Be/PmIthU1vWtx+qh0pXS9+9//+I8yNhqN4gXj4yS5vS6j4H6ZsQaEE0mw3MQAE4pfhKXLd9DgFdI2Or5RQJsNuv7T36ybs4ZeWBd0+kiuJcISQa1bp+NrHBRmsYgmNpcF7k3kw360opyRJE3yJYqioWeSdyMjCHJhagF1crkiTBF1MuJWNVT4PUDiRSTTV/i/axNIvVC6ZJsrIGzdncHQMQsb6+bmhJxSWyjiLWErFgkzPThxwQPi3Ei8mKRSOgxl729apPjkLCqadoT4ePLdX4+F6RMuDDoWE0iRCy8bQ0oz1iobzQWdiBKL4zPfhZ/fv8+P+hrXdeW3z1+juYoK5RWAdDR8MSZZ9t96M0P4n+v5wjDN5EwW42V5yUCIsvTOwin0+W5yCjKOkSYGTu7p/V0aff76enA315obhX+kAt5JLJ7QzcpY7LGKutSWaXzfpgsHPPuUkHGclw0mJau9vLeEyHZrovWrkSUUr6/lPJrpZQvlFKOwOe7pZTTy89/sZTy3uieLyongtUie4dXhoFrEl28hJrs4bCOazLxy1GjC4EboesHf9B3gct7o0RIeX+d1Y9+KwlkslkF+th+NwP1HcEWR+uhO3+yzY/WHAmg6RSvCaoQqE2+zPDemPf3LknEHNMNV3taJJF3Mpl7CXVei4xP/q35XPNT1roeMyfZagl0afyHMXOeeRc2Zq2EIDyVDJbJqvLKGmVZb6MoAhIekcaKOuEV5ZTt7Ax8KTLo+BgbCVJhxN57bG6PyL91r/FYWqsSUUrZKqX8einlm0spO6WUXyqlfJv5zo+VUk4u//2JUsppdN8XVZ1RmwTT91wA7+/HGPlsPIhZvLimBcZaZYMi4V2z8XVVReY3USw7896esiJeDDmcJcfCy0xnlOmZ4h3IFnXPwlzfuVPfITVKpPXmyFtfGyrx8jXQuowpT2M5CuiQ1/Noa/sl5wN91wMDQsmznmyoIVShMcYiF0vay61gbbBreB2N2a5DJvQa3XdM6bDFhcncY38fJ7xnG/Bl5Bp7Z81XghtUk+dw61Yu18O+36byItatRHx3KeVM/f9PlFJ+wnznrJTy3Zf/npRS/mkppfPu+6LBpmrIi3ONXUBWEhaNg6EkShwe/d0TNp6lKkiK3ntHZWLf+Z18w0fvvapFowVCBuo7G9LwxoXc8ho2OHoGE+q1mepICYrybGoF0vPnPKQjSKm2nXGNsiDfrw011SThrlsI14RfavhYeyRQzgg7FDPhKWZERd6rKPylw7G186DfORseYXJOwO+y68E8rAhsjt2Xgch578tyjfb3h9AoSgzfVF7EupWIHyql/A31/3+2lPIz5ju/Ukr5evX/v15KecW778ukRPR9LuxRS5EHBBHaUPv7w0ZhionO6WCblQnq6BBGoZn9/aE07PycJ2tK3kDtu6KNHR3o2XmuSa5kpXerWn99z8eL/o7GzGDT9T3WVfOO3MwCJIQOPo88Zb1mrOu6zzrIrrVVqnS/jFu3MD9H78pgwVdVkFbxRNTcRw7d7e1FmP6a35cyINZ6SkRWGUG5Xh6olCc32PqLLLbhNtZW3ZPRL4Mn4g5QIv6a+c6vAiXij4B7/cVSyudLKZ9/z3ves/433zCNOfQ3MQaPkbwxamWCQXQza7c2G1mPx1oICFMj+65ySIpL24sj1m6w2k0azWf0rHXw0ljBsi6BtE7Btk4PQhYbYVNCWJNda7T28jcPCtqjmuqJGkJgcmMMKbseCC6d5UTZ3zMvGvKM6dJ7tP6oVf26PZhs/dn76uTKrIxeN7VwxrucVmWkSCmoPdyi8Tx7Nq9sqQVJQfX9zAUuG3lMyVv2XRC9aOVyLD+sSyCt6z6eMF7XulyVEF6Fxo5RvBLryO+w90VAWKvcZ9X1jMJ+rOU3+t0Y48nSuvlq3TK6lmqUiG74Pqeu6yallH9cSvlAKeX/KKX8w1LK633f/6r6zr9VSvn2vu/vd133iVLKR/u+/5h33/e973395z//effZjTh96Uul/MZvlPLe95bydV/3okcTj2eV8WZ+K985PCzln/2z1ebla21uMzR2zOt613Xd5+d/vpR790rZ3i7l93+/lJ/92VJee+1rc6ybpJdhjKvSqu/Ifj9GFq1jvt9Na9Z13f/U9/37Ut+NlIjLG36olPIflqFS4+f6vn/cdd1PlUFb+VzXdXullL9VSvmOUspvlVI+0ff9F717NiWiUaNGiN5NwrhRo5eR1q5EbIKaEtGoUaNGjRp97VGNEnFj04Np1KhRo0aNGr07qSkRjRo1atSoUaNR1JSIRo0aNWrUqNEoakpEo0aNGjVq1GgUNSWiUaNGjRo1ajSKmhLRqFGjRo0aNRpFTYlo1KhRo0aNGo2ipkQ0atSoUaNGjUZRUyIaNWrUqFGjRqOoKRGNGjVq1KhRo1HUlIhGjRo1atSo0ShqSkSjRo0aNWrUaBQ1JaJRo0aNGjVqNIqaEtGoUaNGjRo1GkVNiWjUqFGjRo0ajaKmRDRq1KhRo0aNRlFTIho1atSoUaNGo6gpEY0aNWrUqFGjUdSUiEaNGjVq1KjRKOr6vn8xD+66L5VS/rcNPuKVUso/3eD9rzu1+d0stfndLLX53Sy1+d08bXKOv7Hv+6/LfPGFKRGbpq7rPt/3/fte9DjerdTmd7PU5nez1OZ3s9Tmd/P0tTLHLZzRqFGjRo0aNRpFTYlo1KhRo0aNGo2id7MS8ddf9ADe5dTmd7PU5nez1OZ3s9Tmd/P0NTHH79qciEaNGjVq1KjRZund7Ilo1KhRo0aNGm2QXmolouu67++67te6rvtC13VH4PPdrutOLz//xa7r3nv1o3y5KTHHf7nruudd1/1y13V/t+u6b3wR43xZKZpf9b0f6rqu77ruhWdjv0yUmd+u6z52ycO/2nXds6se48tMCfnwnq7r/l7Xdf/oUkZ86EWM82Wlrut+ruu6Wdd1v0I+77que3I5/7/cdd13XvUYS9/3L+VVStkqpfx6KeWbSyk7pZRfKqV8m/nOj5VSTi7//YlSyumLHvfLdCXn+E+XUvYv//2jbY7XO7+X37tZSvn7pZRfKKW870WP+2W5kvz7LaWUf1RK+Vcu//+PvuhxvyxXcn7/einlRy///W2llN940eN+ma5Syr9ZSvnOUsqvkM8/VEr5b0opXSnlT5VSfvGqx/gyeyK+q5Tyhb7vv9j3/f9XSvlPSykfMd/5SCnlb17++++UUj7QdV13hWN82Smc477v/17f9//88n9/oZTy9Vc8xpeZMjxcSimPSin/finld69ycO8CyszvXyil/Ed93/92KaX0fT+74jG+zJSZ376Ucuvy3/9SKeX/vMLxvfTU9/3fL6X8lvOVj5RS/pN+oF8opfzLXdf9q1czuoFeZiXiXyul/O/q/3/z8m/wO33ff7WU8uVSyh+5ktG9Oygzx5rulUErbpSjcH67rvuOUso39H3/X13lwN4llOHfP15K+eNd1/2Drut+oeu677+y0b38lJnff6+U8sNd1/1mKeW/LqV86mqGdm2oVkavnSZX+bA1E/Io2FKTzHcacUrPX9d1P1xKeV8p5f0bHdG7i9z57bruRinlPyil/LmrGtC7jDL8OylDSON7y+BF+x+6rvsTfd//zobH9m6gzPy+Vkp52vf9T3dd992llL91Ob9/sPnhXQt64Wfcy+yJ+M1Syjeo///6suwq+8PvdF03KYM7zXMNNVqkzByXruv+TCnlr5RSbvd9/3tXNLZ3A0Xze7OU8idKKf9913W/UYaY5+dacmWasjLiv+z7/vf7vv9fSym/VgalolFMmfm9V0r5z0oppe/7/7GUsleGng+N1kMpGb1JepmViH9YSvmWruu+qeu6nTIkTn7OfOdzpZQ3Lv/9Q6WU/66/zEZplKJwji/d7f9xGRSIFk+uI3d++77/ct/3r/R9/96+799bhpyT233ff/7FDPelo4yM+C/KkBxcuq57pQzhjS9e6ShfXsrM7z8ppXyglFK6rvvWMigRX7rSUb676XOllE9eVmn8qVLKl/u+/7+ucgAvbTij7/uvdl33oJRyVoYs4Z/r+/5Xu677qVLK5/u+/1wp5WfL4D77Qhk8EJ94cSN++Sg5x8ellMNSyt++zFn9J33f335hg36JKDm/jUZScn7PSimvdl33vJTyL0op/07f9//Pixv1y0PJ+f10KeXtruv+7TK42f9cM+Ty1HXdz5ch1PbKZV7JW6WU7VJK6fv+pAx5Jh8qpXyhlPLPSyk/cuVjbOvZqFGjRo0aNRpDL3M4o1GjRo0aNWr0AqkpEY0aNWrUqFGjUdSUiEaNGjVq1KjRKGpKRKNGjRo1atRoFDUlolGjRo0aNWo0ipoS0ahRo0aNGjUaRU2JaNSoUaNGjRqNoqZENGrUqFGjRo1G0f8P8Z0gDqH/gFMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb8957ef390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pi_estimate(samples=10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can more or less see the contours of the circle forming.  It should look much clearer if we raise the sample count a bit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/john/anaconda/lib/python3.6/site-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
      "  \"matplotlib is currently using a non-GUI backend, \"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate with 100000 samples: 3.1368\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb899114940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pi_estimate(samples=100000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Better!  It's worth taking a moment to consider what we're doing here.  After all, approximating pi (at least to a few decimal points) is a fairly trivial problem.  What's interesting about this technique though is we didn't need to know anything other than basic geometry to get there.  This concept generalizes to much harder problems where no other method of calcuating an answer is known to exist (or where doing so would be computationally intractable).  If sacrificing precision is an acceptable tradeoff, then using Monte Carlo techniques as a general problem-solving framework in domains involving randomness and uncertainty makes a lot of sense.\n",
    "\n",
    "A related use of this technique involves combining Monte Carlo methods with Markov Chains, and is called (appropriately) Markov Chain Monte Carlo (usually abbreviated MCMC).  A full explanation of MCMC is well outside of our scope, but I encourage the reader to check out [this notebook](http://nbviewer.jupyter.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Chapter3_MCMC/Ch3_IntroMCMC_PyMC3.ipynb) for more information (side note: it's part of a whole series on Bayesian methods that is really good, and well worth your time).  In the interest of not adding required reading to understand the next part, I'll try to briefly summarize the idea behind MCMC.\n",
    "\n",
    "Like general Monte Carlo methods, MCMC is fundamentally about sampling from a distribution.  But unlike before, MCMC is an approach to sampling an <b>unknown</b> distribution, given only some existing samples.  MCMC involves using a Markov chain to \"search\" the space of possible distributions in a guided way.  Rather than generating truly random samples, it uses the existing data as a starting point and then \"walks\" a Markov chain toward a state where the chain (hopefully) converges with the real posterior distribution (i.e. the same distribution that the original sample data came from).\n",
    "\n",
    "In a sense, MCMC inverts what we saw above.  In the dice example, we began with a <b>distribution</b> and drew samples to answer some question about that distribution.  With MCMC, we <b>begin</b> with samples from some <b>unknown</b> distribution, and our objective is to approximate, as best we can, the distribution that those samples came from.  This way of thinking about it helps to clarify in what situations we need general Monte Carlo methods vs. MCMC.  If you already have the \"source\" distribution and need to answer some question about it, it's a Monte Carlo problem.  However, if all you have is some data but you don't know the \"source\", then MCMC can help you find it.\n",
    "\n",
    "Let's see an example to make this more concrete.  Imagine we have the result of a series of coin flips and we want to know if the coin being used is unbiased (that is, equally likely to land on heads or tails).  How would you determine this from the data alone?  Let's generate a sequence of coin flips from a coin that we know to be biased so we have some data as a starting point. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "60\n"
     ]
    }
   ],
   "source": [
    "p_heads = 0.6\n",
    "\n",
    "def biased_coin_flip():\n",
    "    if random.random() <= p_heads:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0\n",
    "\n",
    "n_trials = 100\n",
    "coin_flips = [biased_coin_flip() for _ in range(n_trials)]\n",
    "n_heads = sum(coin_flips)\n",
    "print(n_heads)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case since we're producing the data ourselves we know it is biased, but imagine we didn't know where this data came from.  All we know is we have 100 coin flips and 60 are heads.  Obviously 60 is greater than 50, which is what we would guess if the coin was fair.  On the other hand, it's definitely possible to get 60/100 heads with a fair coin just due to randomness.  How do we move from a point estimate to a distribution of the likelihood that the coin is fair?  That's where MCMC comes in."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "Metropolis: [p_interval__]\n",
      "100%|██████████| 100500/100500 [00:08<00:00, 11182.36it/s]\n",
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '15887' (I am process '15888')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /home/john/.theano/compiledir_Linux-4.13--generic-x86_64-with-debian-stretch-sid-x86_64-3.6.4-64/lock_dir\n",
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '15887' (I am process '15889')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /home/john/.theano/compiledir_Linux-4.13--generic-x86_64-with-debian-stretch-sid-x86_64-3.6.4-64/lock_dir\n",
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '15888' (I am process '15889')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /home/john/.theano/compiledir_Linux-4.13--generic-x86_64-with-debian-stretch-sid-x86_64-3.6.4-64/lock_dir\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as coin_model:\n",
    "    p = pm.Uniform('p', lower=0, upper=1)\n",
    "    obs = pm.Bernoulli('obs', p, observed=coin_flips)\n",
    "    step = pm.Metropolis()\n",
    "    trace = pm.sample(100000, step=step)\n",
    "    trace = trace[5000:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Understanding this code requires some background in Bayesian statistics as well as PyMC3.  Very simply, we define a prior distrbution (p) along with an observed variable (obs) representing our known data.  We then configure the algorithm to use (Metropolis-Hastings) and initiate the chain.  The result is a sequence of values that should, in aggregate, represent the most likely distribution that characterizes the original data.\n",
    "\n",
    "To see what we ended up with, we can plot the values in a histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb8827a69e8>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb88805ab00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 9))\n",
    "plt.title('Posterior distribution of $p$')\n",
    "plt.vlines(p_heads, 0, n_trials / 10, linestyle='--', label='true $p$ (unknown)')\n",
    "plt.hist(trace['p'], range=[0.3, 0.9], bins=25, histtype='stepfilled', normed=True)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this result, we can see that the overwhelming likelihood is that the coin is biased.  To actually derive a concrete probability estimate though, we need to specify a range for which we would consider the result \"fair\" and integrate over the probability density function (basically the histogram above).  For the sake of argument, let's say that anything between .45-.55 is fair.  We can then compute the result using a simple count."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.16254736842105263\n"
     ]
    }
   ],
   "source": [
    "n_fair = len(np.where((trace['p'] >= 0.45) & (trace['p'] < 0.55))[0])\n",
    "n_total = len(trace['p'])\n",
    "\n",
    "print(float(n_fair / n_total))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By our definition above, there's roughly a 16% chance that the coin is unbiased!  Hopefully this provides a good illustration of the power and usefulness of MCMC, and Monte Carlo methods more generally."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
